Recently we proposed “quantum language” (or, “the linguistic Copenhagen interpretation of quantum mechanics”, “measurement theory”) as the language of science. This theory asserts the probabilistic interpretatio...Recently we proposed “quantum language” (or, “the linguistic Copenhagen interpretation of quantum mechanics”, “measurement theory”) as the language of science. This theory asserts the probabilistic interpretation of science (=the linguistic quantum mechanical worldview), which is a kind of mathematical generalization of Born’s probabilistic interpretation of quantum mechanics. In this paper, we consider the most fundamental problems in philosophy of science such as Hempel’s raven paradox, Hume’s problem of induction, Goodman’s grue paradox, Peirce’s abduction, flagpole problem, which are closely related to measurement. We believe that these problems can never be solved without the basic theory of science with axioms. Since our worldview (=quantum language) has the axiom concerning measurement, these problems can be solved easily. Thus we believe that quantum language is the central theory in philosophy of science. Hence there is a reason to assert that quantum language gives the mathematical foundations to science.展开更多
The Euler-Bernoulli(E-B)beam theory is combined with Green-Lindsay's(G-L)generalized thermoelasticity theory to analyze the vibration of microbeams.The frequency control equation,based on the two-parameter Winkler...The Euler-Bernoulli(E-B)beam theory is combined with Green-Lindsay's(G-L)generalized thermoelasticity theory to analyze the vibration of microbeams.The frequency control equation,based on the two-parameter Winkler-Pasternak elastic foundation for simply-supported microbeams,is presented.This study investigates the effects of the side-to-thickness ratio and relaxation time parameters on the vibrational natural frequency of thermoelastic microbeam resonators.The frequencies derived from the present model are compared with those from Lord and Shulman's(L-S)theory.The fourthorder solutions for natural vibration frequencies are graphically displayed for comparison.Therefore,attention should be paid to the use of effective foundations to prevent microbeam damage caused by contraction and expansion problems caused by high temperatures.展开更多
We study the conditional entropy of topological dynamical systems using a family of metrics induced by probability bi-sequences.We present a Brin-Katok formula by replacing the mean metric by a family of metrics induc...We study the conditional entropy of topological dynamical systems using a family of metrics induced by probability bi-sequences.We present a Brin-Katok formula by replacing the mean metric by a family of metrics induced by a probability bi-sequence.We also establish the Katok’s entropy formula for conditional entropy for ergodic measures in the case of the new family of metrics.展开更多
This study investigates the dynamics of pneumococcal pneumonia using a novel fractal-fractional Susceptible-Carrier-Infected-Recovered model formulated with the Atangana-Baleanu in Caputo(ABC)sense.Unlike traditional ...This study investigates the dynamics of pneumococcal pneumonia using a novel fractal-fractional Susceptible-Carrier-Infected-Recovered model formulated with the Atangana-Baleanu in Caputo(ABC)sense.Unlike traditional epidemiological models that rely on classical or Caputo fractional derivatives,the proposed model incorporates nonlocal memory effects,hereditary properties,and complex transmission dynamics through fractalfractional calculus.The Atangana-Baleanu operator,with its non-singular Mittag-Leffler kernel,ensures a more realistic representation of disease progression compared to classical integer-order models and singular kernel-based fractional models.The study establishes the existence and uniqueness of the proposed system and conducts a comprehensive stability analysis,including local and global stability.Furthermore,numerical simulations illustrate the effectiveness of the ABC operator in capturing long-memory effects and nonlocal interactions in disease transmission.The results provide valuable insights into public health interventions,particularly in optimizing vaccination strategies,treatment approaches,and mitigation measures.By extending epidemiological modeling through fractal-fractional derivatives,this study offers an advanced framework for analyzing infectious disease dynamics with enhanced accuracy and predictive capabilities.展开更多
This study aims to elucidate the connection between the shape factor of GO(graphene oxide)nanoparticles and the behavior of blood-based non-aligned,2-dimensional,incompressible nanofluid flow near stagnation point,und...This study aims to elucidate the connection between the shape factor of GO(graphene oxide)nanoparticles and the behavior of blood-based non-aligned,2-dimensional,incompressible nanofluid flow near stagnation point,under the influence of temperature-dependent viscosity.Appropriate similarity transformations are employed to transform the non-linear partial differential equations(PDEs)into ordinary differential equations(ODEs).The governing equations are subsequently resolved by utilizing the shooting method.The modified Maxwell model is used to estimate the thermal efficiency of the nanofluid affected by different nanoparticle shapes.The impact of various shapes of GO nanoparticles on the velocity and temperature profiles,along with drag forces and heat flux at the stretching boundary,are examined with particular attention to factors such as viscosity changes.Numerical findings are based on the constant concentration of ϕ=5% with nanoparticles measuring 25 nm in size.The influence of different shapes of GO nanoparticles is analyzed for velocity,temperature distributions,as well as drag forces,and heat transfer at the stretching boundary.The velocity profile is highest for spherical-shaped nanoparticles,whereas the blade-shaped particles produced the greatest temperature distribution.Additionally,itwas observed that enhancing the nanoparticles’volume fraction from 1%to 9%significantly improved the temperature profile.Streamline trends are more inclined to the left when the stretching ratio parameter B=0.7 is applied,and a similar pattern is noted for the variable viscosity case with m=0.5.Furthermore,the blade-shaped nanoparticles exhibit the highest thermal conductivity,while the spherical-shaped nanoparticles display the lowest.展开更多
This study presents a numerical analysis of the steady-state solution for transient magnetohydrodynamic(MHD)dissipative and radiative fluid flow,incorporating an inducedmagnetic field(IMF)and considering a relatively ...This study presents a numerical analysis of the steady-state solution for transient magnetohydrodynamic(MHD)dissipative and radiative fluid flow,incorporating an inducedmagnetic field(IMF)and considering a relatively high concentration of foreign mass(accounting for Soret and Dufour effects)over a vertically oriented semi-infinite plate.The governing equations were normalized using boundary layer(BL)approximations.The resulting nonlinear system of partial differential equations(PDEs)was discretized and solved using an efficient explicit finite difference method(FDM).Numerical simulations were conducted using MATLAB R2015a,and the developed numerical code was verified through comparison with another code written in FORTRAN 6.6a.To ensure the reliability of the results,both mesh refinement and steady-state time validation tests were performed.Furthermore,a comparison with existing published studies was made to confirm the accuracy of the findings.The dimensionless equations revealed the impacts of several key parameters.The IMF initially intensifies near the plate before gradually diminishing as the magnetic parameter increases.For the range 0≤y≤1.8(where y is the horizontal direction),the IMF decreases with a rise in the magnetic Prandtl number;however,for 1.8≤y≤7(approximately),the magnetic field begins to increase.Beyond this,the profile of the magnetic field becomes somewhat irregular through the remaining part of the BL.展开更多
Existing power forecasting models struggle to simultaneously handle high-dimensional,noisy load data while capturing long-term dependencies.This critical limitation necessitates an integrated approach combining dimens...Existing power forecasting models struggle to simultaneously handle high-dimensional,noisy load data while capturing long-term dependencies.This critical limitation necessitates an integrated approach combining dimensionality reduction,temporal modeling,and robust prediction,especially for multi-day forecasting.A novel hybrid model,SLHS-TCN-XGBoost,is proposed for power demand forecasting,leveraging SLHS(dimensionality reduction),TCN(temporal feature learning),and XGBoost(ensemble prediction).Applied to the three-year electricity load dataset of Seoul,South Korea,the model’s MAE,RMSE,and MAPE reached 112.08,148.39,and 2%,respectively,which are significantly reduced in MAE,RMSE,and MAPE by 87.37%,87.35%,and 87.43%relative to the baseline XGBoost model.Performance validation across nine forecast days demonstrates superior accuracy,with MAPE as low as 0.35%and 0.21%on key dates.Statistical Significance tests confirm significant improvements(p<0.05),with the highest MAPE reduction of 98.17%on critical days.Seasonal and temporal error analyses reveal stable performance,particularly in Quarter 3 and Quarter 4(0.5%,0.3%)and nighttime hours(<1%).Robustness tests,including 5-fold cross-validation and Various noise perturbations,confirm the model’s stability and resilience.The SLHS-TCN-XGBoost model offers an efficient and reliable solution for power demand forecasting,with future optimization potential in data preprocessing,algorithm integration,and interpretability.展开更多
In 2012, Ponraj et al. defined a concept of k-product cordial labeling as follows: Let f be a map from V(G)to { 0,1,⋯,k−1 }where k is an integer, 1≤k≤| V(G) |. For each edge uvassign the label f(u)f(v)(modk). f is c...In 2012, Ponraj et al. defined a concept of k-product cordial labeling as follows: Let f be a map from V(G)to { 0,1,⋯,k−1 }where k is an integer, 1≤k≤| V(G) |. For each edge uvassign the label f(u)f(v)(modk). f is called a k-product cordial labeling if | vf(i)−vf(j) |≤1, and | ef(i)−ef(j) |≤1, i,j∈{ 0,1,⋯,k−1 }, where vf(x)and ef(x)denote the number of vertices and edges respectively labeled with x (x=0,1,⋯,k−1). Motivated by this concept, we further studied and established that several families of graphs admit k-product cordial labeling. In this paper, we show that the path graphs Pnadmit k-product cordial labeling.展开更多
The Department of Economic and Social Affairs of the United Nations has released seventeen goals for sustainable development and SDG No.3 is“Good Health and Well-being”,which mainly emphasizes the strategies to be a...The Department of Economic and Social Affairs of the United Nations has released seventeen goals for sustainable development and SDG No.3 is“Good Health and Well-being”,which mainly emphasizes the strategies to be adopted for maintaining a healthy life.The Monkeypox Virus disease was first reported in 1970.Since then,various health initiatives have been taken,including by the WHO.In the present work,we attempt a fractional model of Monkeypox virus disease,which we feel is crucial for a better understanding of this disease.We use the recently introduced ABC fractional derivative to closely examine the Monkeypox virus disease model.The evaluation of this model determines the existence of two equilibrium states.These two stable points exist within the model and include a disease-free equilibrium and endemic equilibrium.The disease-free equilibrium has undergone proof to demonstrate its stability properties.The system remains stable locally and globally whenever the effective reproduction number remains below one.The effective reproduction number becoming greater than unity makes the endemic equilibrium more stable both globally and locally than unity.To comprehensively study the model’s solutions,we employ the Picard-Lindelof approach to investigate their existence and uniqueness.We investigate the Ulam-Hyers and UlamHyers Rassias stability of the fractional order nonlinear framework for the Monkeypox virus disease model.Furthermore,the approximate solutions of the ABC fractional order Monkeypox virus disease model are obtained with the help of a numerical technique combining the Lagrange polynomial interpolation and fundamental theorem of fractional calculus with the ABC fractional derivative.展开更多
The Fe_(1−x)Ni_(x)VO_(4)(x=0,0.05,0.10,and 0.20)nanoparticles in this work were successfully synthesized via a co-precipitation method.The structural,magnetic and electrochemical properties of the prepared Fe_(1−x)Ni_...The Fe_(1−x)Ni_(x)VO_(4)(x=0,0.05,0.10,and 0.20)nanoparticles in this work were successfully synthesized via a co-precipitation method.The structural,magnetic and electrochemical properties of the prepared Fe_(1−x)Ni_(x)VO_(4) nanoparticles were studied as a function of Ni content.The experimental results show that the prepared Ni-doped FeVO_(4) samples have a triclinic structure.Scanning electron microscopy(SEM)images reveal a decrease in average nanoparticle size with increasing Ni content,leading to an enhancement in both specific surface area and magnetization values.X-ray absorption near edge structure(XANES)analysis confirms the substitution of Ni^(2+)ions into Fe^(3+)sites.The magnetic investigation reveals that Ni-doped FeVO_(4) exhibits weak ferromagnetic behavior at room temperature,in contrast to the antiferromagnetic behavior observed in the undoped FeVO_(4).Electrochemical studies demonstrate that the Fe_(0.95)Ni_(0.05)VO_(4) electrode achieves the highest specific capacitance of 334.05 F·g^(−1) at a current density of 1 A·g^(−1),which is attributed to its smallest average pore diameter.In addition,the enhanced specific surface of the Fe_(0.8)Ni_(0.2)VO_(4) electrode is responsible for its outstanding cyclic stability.Overall,our results suggest that the magnetic and electrochemical properties of FeVO_(4) nanoparticles could be effectively tuned by varying Ni doping contents.展开更多
This paper discusses the model of the boundary layer(BL)flow and the heat transfer characteristics of hybrid nanofluid(HNF)over shrinking/stretching disks.In addition,the thermal radiation and the impact of velocity a...This paper discusses the model of the boundary layer(BL)flow and the heat transfer characteristics of hybrid nanofluid(HNF)over shrinking/stretching disks.In addition,the thermal radiation and the impact of velocity and thermal slip boundary conditions are also examined.The considered hybrid nano-fluid contains silver(Ag)and iron oxide(Fe_(3)O_(4))nanoparticles dispersed in the water to prepare the Ag-Fe_(3)O_(4)/water-based hybrid nanofluid.The requisite posited partial differential equations model is converted to ordinary differential equations using similarity transformations.For a numerical solution,the shooting method in Maple is employed.Moreover,the duality in solutions is achieved for both cases of the disk(stretching(λ>0)and shrinking(λ<0)).At the same time,a unique solution is observed for λ=0.No solution is found for them at λ<λ_(c),whereas the solutions are split at the λ=λ_(c).Besides,the value of the λ_(c) is dependent on the φ_(hnf).Meanwhile,the values of f″(0)and -θ′(0)intensified with increasing φ_(hnf).Stability analysis has been applied using bvp4c in MATLAB software due to a dual solution.Furthermore,analysis shows that the first solution is stable and feasible physically.For the slip parameters,an increase in the velocity slip parameter increases the velocity and shear stress profiles while increasing the temperature profile in the first solutions.While the rise in thermal slip parameter reduces the temperature profile nanoparticle volume fractions increase it.展开更多
This study rigorously examines the interplay between viscous dissipation,magnetic effects,and thermal radiation on the flow behavior of a non-Newtonian Carreau squeezed fluid passing by a sensor surface within a micro...This study rigorously examines the interplay between viscous dissipation,magnetic effects,and thermal radiation on the flow behavior of a non-Newtonian Carreau squeezed fluid passing by a sensor surface within a micro cantilever channel,aiming to deepen our understanding of heat transport processes in complex fluid dynamics scenarios.The primary objective is to elucidate how physical operational parameters influence both the velocity of fluid flow and its temperature distribution,utilizing a comprehensive numerical approach.Employing a combination of mathematical modeling techniques,including similarity transformation,this investigation transforms complex partial differential equations into more manageable ordinary ones,subsequently solving them using the homotopy perturbation method.By analyzing the obtained solutions and presenting them graphically,alongside detailed analysis,the study sheds light on the pivotal role of significant parameters in shaping fluid movement and energy distribution.Noteworthy observations reveal a substantial increase in fluid velocity with escalating magnetic parameters,while conversely,a contrasting trend emerges in the temperature distribution,highlighting the intricate relationship between magnetic effects,flow dynamics,and thermal behavior in non-Newtonian fluids.Further,the suction velocity enhance both the local skin friction and Nusselt numbers,whereas theWeissenberg number reduces them,opposite to the effect of the power-law index.展开更多
Reconfiguration,as well as optimal utilization of distributed generation sources and capacitor banks,are highly effective methods for reducing losses and improving the voltage profile,or in other words,the power quali...Reconfiguration,as well as optimal utilization of distributed generation sources and capacitor banks,are highly effective methods for reducing losses and improving the voltage profile,or in other words,the power quality in the power distribution system.Researchers have considered the use of distributed generation resources in recent years.There are numerous advantages to utilizing these resources,the most significant of which are the reduction of network losses and enhancement of voltage stability.Non-dominated Sorting Genetic Algorithm II(NSGA-II),Multi-Objective Particle Swarm Optimization(MOPSO),and Intersect Mutation Differential Evolution(IMDE)algorithms are used in this paper to perform optimal reconfiguration,simultaneous location,and capacity determination of distributed generation resources and capacitor banks.Three scenarios were used to replicate the studies.The reconfiguration of the switches,as well as the location and determination of the capacitor bank’s optimal capacity,were investigated in this scenario.However,in the third scenario,reconfiguration,and determining the location and capacity of the Distributed Generation(DG)resources and capacitor banks have been carried out simultaneously.Finally,the simulation results of these three algorithms are compared.The results indicate that the proposed NSGAII algorithm outperformed the other two multi-objective algorithms and was capable of maintaining smaller objective functions in all scenarios.Specifically,the energy losses were reduced from 211 to 51.35 kW(a 75.66%reduction),119.13 kW(a 43.54%reduction),and 23.13 kW(an 89.04%reduction),while the voltage stability index(VSI)decreased from 6.96 to 2.105,1.239,and 1.257,respectively,demonstrating significant improvement in the voltage profile.展开更多
The need for efficient thermal energy systems has gained significant attention due to the growing global concern about renewable energy resources,particularly in residential buildings.One of the biggest challenges in ...The need for efficient thermal energy systems has gained significant attention due to the growing global concern about renewable energy resources,particularly in residential buildings.One of the biggest challenges in this area is capturing and converting solar energy at maximum efficiency.This requires the use of strong materials and advanced fluids to enhance conversion efficiency while minimizing energy losses.Despite extensive research on thermal energy systems,there remains a limited understanding of how the combined effects of thermal radiation,irreversibility processes,and advanced heat flux models contribute to optimizing solar power performance in residential applications.Addressing these knowledge gaps is critical for advancing the design and implementation of highly efficient thermal energy systems.Owing to its usage,this study investigates the thermal energy and irreversibility processes in the context of solar power systems for residential buildings.Specifically,it explores the influence of thermal radiation and the Cattaneo–Christov heat flux model,considering the interactions over a stretching surface.The study incorporates cross fluid and Maxwell fluid effects into the governing model equations.Utilizing the Galerkin-weighted residual method,the transformed model is solved to understand the impacts on heat distribution.The findings reveal that increased thermal radiation and thermal conductivity significantly enhance heat distribution,offering valuable insights for optimizing solar power system efficiency in residential applications.展开更多
In this paper, the Adomian＇s decomposition method （ADM） is presented for finding the exact solutions of a more general biological population models. A new solution is constructed in power series. The fractional der...In this paper, the Adomian＇s decomposition method （ADM） is presented for finding the exact solutions of a more general biological population models. A new solution is constructed in power series. The fractional derivatives are described in the Caputo sense. To illustrate the reliability of the method, some examples are provided.展开更多
This article is concerned with the effect of rotation on the general model of the equations of the generalized thermoe- lasticity for a homogeneous isotropic elastic half-space solid, whose surface is subjected to a M...This article is concerned with the effect of rotation on the general model of the equations of the generalized thermoe- lasticity for a homogeneous isotropic elastic half-space solid, whose surface is subjected to a Mode-I crack problem. The fractional order theory of thermoelasticity is used to obtain the analytical solutions for displacement components, force stresses, and temperature. The boundary of the crack is subjected to a prescribed stress distribution and temperature. The normal mode analysis technique is used to solve the resulting non-dimensional coupled governing equations of the problem. The variations of the considered variables with the horizontal distance are illustrated graphically. Some particular cases are also discussed in the context of the problem. Effects of the fractional parameter, reinforcement, and rotation on the varia- tions of different field quantities inside the elastic medium are analyzed graphically. Comparisons are made between the results in the presence and those in the absence of fiber-reinforcing, rotating and fractional parameters.展开更多
The modified simple equation method is employed to construct the exact solutions involving parameters of nonlinear evolution equations via the (1+1)-dimensional modified KdV equation,and the (1+1)-dimensional reaction...The modified simple equation method is employed to construct the exact solutions involving parameters of nonlinear evolution equations via the (1+1)-dimensional modified KdV equation,and the (1+1)-dimensional reaction-diffusion equation.When these parameters are taken to be special values,the solitary wave solutions are derived from the exact solutions.It is shown that the proposed method provides a more powerful mathematical tool for solving nonlinear evolution equations in mathematical physics.展开更多
Applying Nevanlinna theory of the value distribution of meromorphic functions, we mainly study the growth and some other properties of meromorphic solutions of the type of system of complex differential and difference...Applying Nevanlinna theory of the value distribution of meromorphic functions, we mainly study the growth and some other properties of meromorphic solutions of the type of system of complex differential and difference equations of the following form {j=1∑nαj（z）f1（λj1）（z＋cj）=R2（z,f2（z））,j=1∑nβj（z）f2（λj2）（z＋cj）=R1（z,f1（z））. where λij （j = 1, 2,…, n; i = 1, 2） are finite non-negative integers, and cj （j = 1, 2,… , n） are distinct, nonzero complex numbers, αj（z）, βj（z） （j = 1,2,… ,n） are small functions relative to fi（z） （i =1, 2） respectively, Ri（z, f（z）） （i = 1, 2） are rational in fi（z） （i =1, 2） with coefficients which are small functions of fi（z） （i = 1, 2） respectively.展开更多
In this paper, we study a boundary value problem of nonlinear fractional dif- ferential equations of order q （1 〈 q 〈 2） with non-separated integral boundary conditions. Some new existence and uniqueness results a...In this paper, we study a boundary value problem of nonlinear fractional dif- ferential equations of order q （1 〈 q 〈 2） with non-separated integral boundary conditions. Some new existence and uniqueness results are obtained by using some standard fixed point theorems and Leray-Schauder degree theory. Some illustrative examples are also presented. We extend previous results even in the integer case q = 2.展开更多
In this article,the reduced differential transform method is introduced to solve the nonlinear fractional model of Tumor-Immune.The fractional derivatives are described in the Caputo sense.The solutions derived using ...In this article,the reduced differential transform method is introduced to solve the nonlinear fractional model of Tumor-Immune.The fractional derivatives are described in the Caputo sense.The solutions derived using this method are easy and very accurate.The model is given by its signal flow diagram.Moreover,a simulation of the system by the Simulink of MATLAB is given.The disease-free equilibrium and stability of the equilibrium point are calculated.Formulation of a fractional optimal control for the cancer model is calculated.In addition,to control the system,we propose a novel modification of its model.This modification is based on converting the model to a memristive one,which is a first time in the literature that such idea is used to control this type of diseases.Also,we study the system’s stability via the Lyapunov exponents and Poincare maps before and after control.Fractional order differential equations(FDEs)are commonly utilized to model systems that have memory,and exist in several physical phenomena,models in thermoelasticity field,and biological paradigms.FDEs have been utilized to model the realistic biphasic decline manner of elastic systems and infection of diseases with a slower rate of change.FDEs are more useful than integer-order in modeling sophisticated models that contain physical phenomena.展开更多
文摘Recently we proposed “quantum language” (or, “the linguistic Copenhagen interpretation of quantum mechanics”, “measurement theory”) as the language of science. This theory asserts the probabilistic interpretation of science (=the linguistic quantum mechanical worldview), which is a kind of mathematical generalization of Born’s probabilistic interpretation of quantum mechanics. In this paper, we consider the most fundamental problems in philosophy of science such as Hempel’s raven paradox, Hume’s problem of induction, Goodman’s grue paradox, Peirce’s abduction, flagpole problem, which are closely related to measurement. We believe that these problems can never be solved without the basic theory of science with axioms. Since our worldview (=quantum language) has the axiom concerning measurement, these problems can be solved easily. Thus we believe that quantum language is the central theory in philosophy of science. Hence there is a reason to assert that quantum language gives the mathematical foundations to science.
基金the Deanship of Research and Graduate Studies at King Khalid University for funding this work through a large research project(No.RGP2/80/45)。
文摘The Euler-Bernoulli(E-B)beam theory is combined with Green-Lindsay's(G-L)generalized thermoelasticity theory to analyze the vibration of microbeams.The frequency control equation,based on the two-parameter Winkler-Pasternak elastic foundation for simply-supported microbeams,is presented.This study investigates the effects of the side-to-thickness ratio and relaxation time parameters on the vibrational natural frequency of thermoelastic microbeam resonators.The frequencies derived from the present model are compared with those from Lord and Shulman's(L-S)theory.The fourthorder solutions for natural vibration frequencies are graphically displayed for comparison.Therefore,attention should be paid to the use of effective foundations to prevent microbeam damage caused by contraction and expansion problems caused by high temperatures.
文摘We study the conditional entropy of topological dynamical systems using a family of metrics induced by probability bi-sequences.We present a Brin-Katok formula by replacing the mean metric by a family of metrics induced by a probability bi-sequence.We also establish the Katok’s entropy formula for conditional entropy for ergodic measures in the case of the new family of metrics.
基金funded by the Research,Development,and Innovation Authority(RDIA)-Kingdom of Saudi Arabia-with grant number 12803-baha-2023-BU-R-3-1-EI.
文摘This study investigates the dynamics of pneumococcal pneumonia using a novel fractal-fractional Susceptible-Carrier-Infected-Recovered model formulated with the Atangana-Baleanu in Caputo(ABC)sense.Unlike traditional epidemiological models that rely on classical or Caputo fractional derivatives,the proposed model incorporates nonlocal memory effects,hereditary properties,and complex transmission dynamics through fractalfractional calculus.The Atangana-Baleanu operator,with its non-singular Mittag-Leffler kernel,ensures a more realistic representation of disease progression compared to classical integer-order models and singular kernel-based fractional models.The study establishes the existence and uniqueness of the proposed system and conducts a comprehensive stability analysis,including local and global stability.Furthermore,numerical simulations illustrate the effectiveness of the ABC operator in capturing long-memory effects and nonlocal interactions in disease transmission.The results provide valuable insights into public health interventions,particularly in optimizing vaccination strategies,treatment approaches,and mitigation measures.By extending epidemiological modeling through fractal-fractional derivatives,this study offers an advanced framework for analyzing infectious disease dynamics with enhanced accuracy and predictive capabilities.
文摘This study aims to elucidate the connection between the shape factor of GO(graphene oxide)nanoparticles and the behavior of blood-based non-aligned,2-dimensional,incompressible nanofluid flow near stagnation point,under the influence of temperature-dependent viscosity.Appropriate similarity transformations are employed to transform the non-linear partial differential equations(PDEs)into ordinary differential equations(ODEs).The governing equations are subsequently resolved by utilizing the shooting method.The modified Maxwell model is used to estimate the thermal efficiency of the nanofluid affected by different nanoparticle shapes.The impact of various shapes of GO nanoparticles on the velocity and temperature profiles,along with drag forces and heat flux at the stretching boundary,are examined with particular attention to factors such as viscosity changes.Numerical findings are based on the constant concentration of ϕ=5% with nanoparticles measuring 25 nm in size.The influence of different shapes of GO nanoparticles is analyzed for velocity,temperature distributions,as well as drag forces,and heat transfer at the stretching boundary.The velocity profile is highest for spherical-shaped nanoparticles,whereas the blade-shaped particles produced the greatest temperature distribution.Additionally,itwas observed that enhancing the nanoparticles’volume fraction from 1%to 9%significantly improved the temperature profile.Streamline trends are more inclined to the left when the stretching ratio parameter B=0.7 is applied,and a similar pattern is noted for the variable viscosity case with m=0.5.Furthermore,the blade-shaped nanoparticles exhibit the highest thermal conductivity,while the spherical-shaped nanoparticles display the lowest.
基金supported by the NST Fellowship under the Ministry of Science and Technology,Government of the People’s Republic of Bangladesh(Session:2019–2020,merit number:334,serial number:714,physical science).
文摘This study presents a numerical analysis of the steady-state solution for transient magnetohydrodynamic(MHD)dissipative and radiative fluid flow,incorporating an inducedmagnetic field(IMF)and considering a relatively high concentration of foreign mass(accounting for Soret and Dufour effects)over a vertically oriented semi-infinite plate.The governing equations were normalized using boundary layer(BL)approximations.The resulting nonlinear system of partial differential equations(PDEs)was discretized and solved using an efficient explicit finite difference method(FDM).Numerical simulations were conducted using MATLAB R2015a,and the developed numerical code was verified through comparison with another code written in FORTRAN 6.6a.To ensure the reliability of the results,both mesh refinement and steady-state time validation tests were performed.Furthermore,a comparison with existing published studies was made to confirm the accuracy of the findings.The dimensionless equations revealed the impacts of several key parameters.The IMF initially intensifies near the plate before gradually diminishing as the magnetic parameter increases.For the range 0≤y≤1.8(where y is the horizontal direction),the IMF decreases with a rise in the magnetic Prandtl number;however,for 1.8≤y≤7(approximately),the magnetic field begins to increase.Beyond this,the profile of the magnetic field becomes somewhat irregular through the remaining part of the BL.
基金supported by Mahasarakham University for Piyapatr Busababodhin’s work.Guoqing Chen’s research was supported by Chengdu Jincheng College Green Data Integration Intelligence Research and Innovation Project(No.2025-2027)the High-Quality Development Research Center Project in the Tuojiang River Basin(No.TJGZL2024-07)+1 种基金the Open Fund ofWuhan Gravitation and Solid Earth Tides,National Observation and Research Station(No.WHYWZ202406)the Scientific Research Fund of the Institute of Seismology,CEA,and the National Institute of Natural Hazards,MEM(No.IS202236328).
文摘Existing power forecasting models struggle to simultaneously handle high-dimensional,noisy load data while capturing long-term dependencies.This critical limitation necessitates an integrated approach combining dimensionality reduction,temporal modeling,and robust prediction,especially for multi-day forecasting.A novel hybrid model,SLHS-TCN-XGBoost,is proposed for power demand forecasting,leveraging SLHS(dimensionality reduction),TCN(temporal feature learning),and XGBoost(ensemble prediction).Applied to the three-year electricity load dataset of Seoul,South Korea,the model’s MAE,RMSE,and MAPE reached 112.08,148.39,and 2%,respectively,which are significantly reduced in MAE,RMSE,and MAPE by 87.37%,87.35%,and 87.43%relative to the baseline XGBoost model.Performance validation across nine forecast days demonstrates superior accuracy,with MAPE as low as 0.35%and 0.21%on key dates.Statistical Significance tests confirm significant improvements(p<0.05),with the highest MAPE reduction of 98.17%on critical days.Seasonal and temporal error analyses reveal stable performance,particularly in Quarter 3 and Quarter 4(0.5%,0.3%)and nighttime hours(<1%).Robustness tests,including 5-fold cross-validation and Various noise perturbations,confirm the model’s stability and resilience.The SLHS-TCN-XGBoost model offers an efficient and reliable solution for power demand forecasting,with future optimization potential in data preprocessing,algorithm integration,and interpretability.
文摘In 2012, Ponraj et al. defined a concept of k-product cordial labeling as follows: Let f be a map from V(G)to { 0,1,⋯,k−1 }where k is an integer, 1≤k≤| V(G) |. For each edge uvassign the label f(u)f(v)(modk). f is called a k-product cordial labeling if | vf(i)−vf(j) |≤1, and | ef(i)−ef(j) |≤1, i,j∈{ 0,1,⋯,k−1 }, where vf(x)and ef(x)denote the number of vertices and edges respectively labeled with x (x=0,1,⋯,k−1). Motivated by this concept, we further studied and established that several families of graphs admit k-product cordial labeling. In this paper, we show that the path graphs Pnadmit k-product cordial labeling.
基金sponsored by Prince Sattam Bin Abulaziz University(PSAU)as part of funding for its SDG Roadmap Research Funding Programme Project Number PSAU-2023-SDG-107.
文摘The Department of Economic and Social Affairs of the United Nations has released seventeen goals for sustainable development and SDG No.3 is“Good Health and Well-being”,which mainly emphasizes the strategies to be adopted for maintaining a healthy life.The Monkeypox Virus disease was first reported in 1970.Since then,various health initiatives have been taken,including by the WHO.In the present work,we attempt a fractional model of Monkeypox virus disease,which we feel is crucial for a better understanding of this disease.We use the recently introduced ABC fractional derivative to closely examine the Monkeypox virus disease model.The evaluation of this model determines the existence of two equilibrium states.These two stable points exist within the model and include a disease-free equilibrium and endemic equilibrium.The disease-free equilibrium has undergone proof to demonstrate its stability properties.The system remains stable locally and globally whenever the effective reproduction number remains below one.The effective reproduction number becoming greater than unity makes the endemic equilibrium more stable both globally and locally than unity.To comprehensively study the model’s solutions,we employ the Picard-Lindelof approach to investigate their existence and uniqueness.We investigate the Ulam-Hyers and UlamHyers Rassias stability of the fractional order nonlinear framework for the Monkeypox virus disease model.Furthermore,the approximate solutions of the ABC fractional order Monkeypox virus disease model are obtained with the help of a numerical technique combining the Lagrange polynomial interpolation and fundamental theorem of fractional calculus with the ABC fractional derivative.
文摘The Fe_(1−x)Ni_(x)VO_(4)(x=0,0.05,0.10,and 0.20)nanoparticles in this work were successfully synthesized via a co-precipitation method.The structural,magnetic and electrochemical properties of the prepared Fe_(1−x)Ni_(x)VO_(4) nanoparticles were studied as a function of Ni content.The experimental results show that the prepared Ni-doped FeVO_(4) samples have a triclinic structure.Scanning electron microscopy(SEM)images reveal a decrease in average nanoparticle size with increasing Ni content,leading to an enhancement in both specific surface area and magnetization values.X-ray absorption near edge structure(XANES)analysis confirms the substitution of Ni^(2+)ions into Fe^(3+)sites.The magnetic investigation reveals that Ni-doped FeVO_(4) exhibits weak ferromagnetic behavior at room temperature,in contrast to the antiferromagnetic behavior observed in the undoped FeVO_(4).Electrochemical studies demonstrate that the Fe_(0.95)Ni_(0.05)VO_(4) electrode achieves the highest specific capacitance of 334.05 F·g^(−1) at a current density of 1 A·g^(−1),which is attributed to its smallest average pore diameter.In addition,the enhanced specific surface of the Fe_(0.8)Ni_(0.2)VO_(4) electrode is responsible for its outstanding cyclic stability.Overall,our results suggest that the magnetic and electrochemical properties of FeVO_(4) nanoparticles could be effectively tuned by varying Ni doping contents.
基金the Researchers Supporting Project number(RSPD2025R997),King Saud University,Riyadh,Saudi Arabia.
文摘This paper discusses the model of the boundary layer(BL)flow and the heat transfer characteristics of hybrid nanofluid(HNF)over shrinking/stretching disks.In addition,the thermal radiation and the impact of velocity and thermal slip boundary conditions are also examined.The considered hybrid nano-fluid contains silver(Ag)and iron oxide(Fe_(3)O_(4))nanoparticles dispersed in the water to prepare the Ag-Fe_(3)O_(4)/water-based hybrid nanofluid.The requisite posited partial differential equations model is converted to ordinary differential equations using similarity transformations.For a numerical solution,the shooting method in Maple is employed.Moreover,the duality in solutions is achieved for both cases of the disk(stretching(λ>0)and shrinking(λ<0)).At the same time,a unique solution is observed for λ=0.No solution is found for them at λ<λ_(c),whereas the solutions are split at the λ=λ_(c).Besides,the value of the λ_(c) is dependent on the φ_(hnf).Meanwhile,the values of f″(0)and -θ′(0)intensified with increasing φ_(hnf).Stability analysis has been applied using bvp4c in MATLAB software due to a dual solution.Furthermore,analysis shows that the first solution is stable and feasible physically.For the slip parameters,an increase in the velocity slip parameter increases the velocity and shear stress profiles while increasing the temperature profile in the first solutions.While the rise in thermal slip parameter reduces the temperature profile nanoparticle volume fractions increase it.
文摘This study rigorously examines the interplay between viscous dissipation,magnetic effects,and thermal radiation on the flow behavior of a non-Newtonian Carreau squeezed fluid passing by a sensor surface within a micro cantilever channel,aiming to deepen our understanding of heat transport processes in complex fluid dynamics scenarios.The primary objective is to elucidate how physical operational parameters influence both the velocity of fluid flow and its temperature distribution,utilizing a comprehensive numerical approach.Employing a combination of mathematical modeling techniques,including similarity transformation,this investigation transforms complex partial differential equations into more manageable ordinary ones,subsequently solving them using the homotopy perturbation method.By analyzing the obtained solutions and presenting them graphically,alongside detailed analysis,the study sheds light on the pivotal role of significant parameters in shaping fluid movement and energy distribution.Noteworthy observations reveal a substantial increase in fluid velocity with escalating magnetic parameters,while conversely,a contrasting trend emerges in the temperature distribution,highlighting the intricate relationship between magnetic effects,flow dynamics,and thermal behavior in non-Newtonian fluids.Further,the suction velocity enhance both the local skin friction and Nusselt numbers,whereas theWeissenberg number reduces them,opposite to the effect of the power-law index.
文摘Reconfiguration,as well as optimal utilization of distributed generation sources and capacitor banks,are highly effective methods for reducing losses and improving the voltage profile,or in other words,the power quality in the power distribution system.Researchers have considered the use of distributed generation resources in recent years.There are numerous advantages to utilizing these resources,the most significant of which are the reduction of network losses and enhancement of voltage stability.Non-dominated Sorting Genetic Algorithm II(NSGA-II),Multi-Objective Particle Swarm Optimization(MOPSO),and Intersect Mutation Differential Evolution(IMDE)algorithms are used in this paper to perform optimal reconfiguration,simultaneous location,and capacity determination of distributed generation resources and capacitor banks.Three scenarios were used to replicate the studies.The reconfiguration of the switches,as well as the location and determination of the capacitor bank’s optimal capacity,were investigated in this scenario.However,in the third scenario,reconfiguration,and determining the location and capacity of the Distributed Generation(DG)resources and capacitor banks have been carried out simultaneously.Finally,the simulation results of these three algorithms are compared.The results indicate that the proposed NSGAII algorithm outperformed the other two multi-objective algorithms and was capable of maintaining smaller objective functions in all scenarios.Specifically,the energy losses were reduced from 211 to 51.35 kW(a 75.66%reduction),119.13 kW(a 43.54%reduction),and 23.13 kW(an 89.04%reduction),while the voltage stability index(VSI)decreased from 6.96 to 2.105,1.239,and 1.257,respectively,demonstrating significant improvement in the voltage profile.
基金funded by Universiti Teknikal Malaysia Melaka through the Tabung Penerbitan Jurnal(S11017).
文摘The need for efficient thermal energy systems has gained significant attention due to the growing global concern about renewable energy resources,particularly in residential buildings.One of the biggest challenges in this area is capturing and converting solar energy at maximum efficiency.This requires the use of strong materials and advanced fluids to enhance conversion efficiency while minimizing energy losses.Despite extensive research on thermal energy systems,there remains a limited understanding of how the combined effects of thermal radiation,irreversibility processes,and advanced heat flux models contribute to optimizing solar power performance in residential applications.Addressing these knowledge gaps is critical for advancing the design and implementation of highly efficient thermal energy systems.Owing to its usage,this study investigates the thermal energy and irreversibility processes in the context of solar power systems for residential buildings.Specifically,it explores the influence of thermal radiation and the Cattaneo–Christov heat flux model,considering the interactions over a stretching surface.The study incorporates cross fluid and Maxwell fluid effects into the governing model equations.Utilizing the Galerkin-weighted residual method,the transformed model is solved to understand the impacts on heat distribution.The findings reveal that increased thermal radiation and thermal conductivity significantly enhance heat distribution,offering valuable insights for optimizing solar power system efficiency in residential applications.
文摘In this paper, the Adomian＇s decomposition method （ADM） is presented for finding the exact solutions of a more general biological population models. A new solution is constructed in power series. The fractional derivatives are described in the Caputo sense. To illustrate the reliability of the method, some examples are provided.
文摘This article is concerned with the effect of rotation on the general model of the equations of the generalized thermoe- lasticity for a homogeneous isotropic elastic half-space solid, whose surface is subjected to a Mode-I crack problem. The fractional order theory of thermoelasticity is used to obtain the analytical solutions for displacement components, force stresses, and temperature. The boundary of the crack is subjected to a prescribed stress distribution and temperature. The normal mode analysis technique is used to solve the resulting non-dimensional coupled governing equations of the problem. The variations of the considered variables with the horizontal distance are illustrated graphically. Some particular cases are also discussed in the context of the problem. Effects of the fractional parameter, reinforcement, and rotation on the varia- tions of different field quantities inside the elastic medium are analyzed graphically. Comparisons are made between the results in the presence and those in the absence of fiber-reinforcing, rotating and fractional parameters.
文摘The modified simple equation method is employed to construct the exact solutions involving parameters of nonlinear evolution equations via the (1+1)-dimensional modified KdV equation,and the (1+1)-dimensional reaction-diffusion equation.When these parameters are taken to be special values,the solitary wave solutions are derived from the exact solutions.It is shown that the proposed method provides a more powerful mathematical tool for solving nonlinear evolution equations in mathematical physics.
基金supported by the National Natural Science Foundation of China(10471067)NSF of Guangdong Province(04010474)
文摘Applying Nevanlinna theory of the value distribution of meromorphic functions, we mainly study the growth and some other properties of meromorphic solutions of the type of system of complex differential and difference equations of the following form {j=1∑nαj（z）f1（λj1）（z＋cj）=R2（z,f2（z））,j=1∑nβj（z）f2（λj2）（z＋cj）=R1（z,f1（z））. where λij （j = 1, 2,…, n; i = 1, 2） are finite non-negative integers, and cj （j = 1, 2,… , n） are distinct, nonzero complex numbers, αj（z）, βj（z） （j = 1,2,… ,n） are small functions relative to fi（z） （i =1, 2） respectively, Ri（z, f（z）） （i = 1, 2） are rational in fi（z） （i =1, 2） with coefficients which are small functions of fi（z） （i = 1, 2） respectively.
文摘In this paper, we study a boundary value problem of nonlinear fractional dif- ferential equations of order q （1 〈 q 〈 2） with non-separated integral boundary conditions. Some new existence and uniqueness results are obtained by using some standard fixed point theorems and Leray-Schauder degree theory. Some illustrative examples are also presented. We extend previous results even in the integer case q = 2.
基金funded by“Taif University Researchers Supporting Project number(TURSP-2020/160),Taif University,Taif,Saudi Arabia”.
文摘In this article,the reduced differential transform method is introduced to solve the nonlinear fractional model of Tumor-Immune.The fractional derivatives are described in the Caputo sense.The solutions derived using this method are easy and very accurate.The model is given by its signal flow diagram.Moreover,a simulation of the system by the Simulink of MATLAB is given.The disease-free equilibrium and stability of the equilibrium point are calculated.Formulation of a fractional optimal control for the cancer model is calculated.In addition,to control the system,we propose a novel modification of its model.This modification is based on converting the model to a memristive one,which is a first time in the literature that such idea is used to control this type of diseases.Also,we study the system’s stability via the Lyapunov exponents and Poincare maps before and after control.Fractional order differential equations(FDEs)are commonly utilized to model systems that have memory,and exist in several physical phenomena,models in thermoelasticity field,and biological paradigms.FDEs have been utilized to model the realistic biphasic decline manner of elastic systems and infection of diseases with a slower rate of change.FDEs are more useful than integer-order in modeling sophisticated models that contain physical phenomena.
