We propose a mathematical model of the coronavirus disease 2019(COVID-19)to investigate the transmission and control mechanism of the disease in the community of Nigeria.Using stability theory of differential equation...We propose a mathematical model of the coronavirus disease 2019(COVID-19)to investigate the transmission and control mechanism of the disease in the community of Nigeria.Using stability theory of differential equations,the qualitative behavior of model is studied.The pandemic indicator represented by basic reproductive number R0 is obtained from the largest eigenvalue of the next-generation matrix.Local as well as global asymptotic stability conditions for the disease-free and pandemic equilibrium are obtained which determines the conditions to stabilize the exponential spread of the disease.Further,we examined this model by using Atangana–Baleanu fractional derivative operator and existence criteria of solution for the operator is established.We consider the data of reported infection cases from April 1,2020,till April 30,2020,and parameterized the model.We have used one of the reliable and efficient method known as iterative Laplace transform to obtain numerical simulations.The impacts of various biological parameters on transmission dynamics of COVID-19 is examined.These results are based on different values of the fractional parameter and serve as a control parameter to identify the significant strategies for the control of the disease.In the end,the obtained results are demonstrated graphically to justify our theoretical findings.展开更多
It is a very difficult task for the researchers to find the exact solutions to mathematical problems that contain non-linear terms in the equation.Therefore,this article aims to investigate the viscous dissipation(VD)...It is a very difficult task for the researchers to find the exact solutions to mathematical problems that contain non-linear terms in the equation.Therefore,this article aims to investigate the viscous dissipation(VD)effect on the fractional model of Jeffrey fluid over a heated vertical flat plate that suddenly moves in its own plane.Based on the Atangana-Baleanu operator,the fractional model is developed from the fractional constitutive equations.VD is responsible for the non-linear behavior in the problem.Upon taking the Laplace and Fourier sine transforms,exact expressions have been obtained for momentum and energy equations.The influence of relative parameters on fluid flow and temperature distribution is shown graphically.As special cases,and for the sake of correctness,the corresponding results for second-grade fluid and Newtonian viscous fluid are also obtained.It is interesting to note that fractional parameterαprovides more than one line as compared to the classical model.This effect represents the memory effect in the fluid which is not possible to elaborate by the classical model.It is also worth noting that the temperature profile of the generalized Jeffrey fluid rises for higher values of Eckert number which is due to the enthalpy difference of the boundary layer.展开更多
In this paper,we study two fractional models in the Caputo–Fabrizio sense and Atangana–Baleanu sense,in which the effects of malaria infection on mosquito biting behavior and attractiveness of humans are considered....In this paper,we study two fractional models in the Caputo–Fabrizio sense and Atangana–Baleanu sense,in which the effects of malaria infection on mosquito biting behavior and attractiveness of humans are considered.Using Lyapunov theory,we prove the global asymptotic stability of the unique endemic equilibrium of the integer-order model,and the fractional models,whenever the basic reproduction number R0 is greater than one.By using fixed point theory,we prove existence,and conditions of the uniqueness of solutions,as well as the stability and convergence of numerical schemes.Numerical simulations for both models,using fractional Euler method and Adams–Bashforth method,respectively,are provided to confirm the effectiveness of used approximation methods for different values of the fractional-orderγ.展开更多
New atypical pneumonia caused by a virus called Coronavirus(COVID-19)appeared in Wuhan,China in December 2019.Unlike previous epidemics due to the severe acute respiratory syndrome(SARS)and the Middle East respiratory...New atypical pneumonia caused by a virus called Coronavirus(COVID-19)appeared in Wuhan,China in December 2019.Unlike previous epidemics due to the severe acute respiratory syndrome(SARS)and the Middle East respiratory syndrome coronavirus(MERS-CoV),COVID-19 has the particularity that it is more contagious than the other previous ones.In this paper,we try to predict the COVID-19 epidemic peak in Japan with the help of real-time data from January 15 to February 29,2020 with the uses of fractional derivatives,namely,Caputo derivatives,the Caputo–Fabrizio derivatives,and Atangana–Baleanu derivatives in the Caputo sense.The fixed point theory and Picard–Lindel of approach used in this study provide the proof for the existence and uniqueness analysis of the solutions to the noninteger-order models under the investi-gations.For each fractional model,we propose a numerical scheme as well as prove its stability.Using parameter values estimated from the Japan COVID-19 epidemic real data,we perform numerical simulations to confirm the effectiveness of used approxima-tion methods by numerical simulations for different values of the fractional-orderγ,and to give the predictions of COVID-19 epidemic peaks in Japan in a specific range of time intervals.展开更多
Because of the features involved with their varied kernels,differential operators relying on convolution formulations have been acknowledged as effective mathematical resources for modeling real-world issues.In this p...Because of the features involved with their varied kernels,differential operators relying on convolution formulations have been acknowledged as effective mathematical resources for modeling real-world issues.In this paper,we constructed a stochastic fractional framework of measles spreading mechanisms with dual medication immunization considering the exponential decay and Mittag-Leffler kernels.In this approach,the overall population was separated into five cohorts.Furthermore,the descriptive behavior of the system was investigated,including prerequisites for the positivity of solutions,invariant domain of the solution,presence and stability of equilibrium points,and sensitivity analysis.We included a stochastic element in every cohort and employed linear growth and Lipschitz criteria to show the existence and uniqueness of solutions.Several numerical simulations for various fractional orders and randomization intensities are illustrated.展开更多
Fractional calculus has drawn more attentions of mathematicians and engineers in recent years.A lot of new fractional operators were used to handle various practical problems.In this article,we mainly study four new f...Fractional calculus has drawn more attentions of mathematicians and engineers in recent years.A lot of new fractional operators were used to handle various practical problems.In this article,we mainly study four new fractional operators,namely the CaputoFabrizio operator,the Atangana-Baleanu operator,the Sun-Hao-Zhang-Baleanu operator and the generalized Caputo type operator under the frame of the k-Prabhakar fractional integral operator.Usually,the theory of the k-Prabhakar fractional integral is regarded as a much broader than classical fractional operator.Here,we firstly give a series expansion of the k-Prabhakar fractional integral by means of the k-Riemann-Liouville integral.Then,a connection between the k-Prabhakar fractional integral and the four new fractional operators of the above mentioned was shown,respectively.In terms of the above analysis,we can obtain this a basic fact that it only needs to consider the k-Prabhakar fractional integral to cover these results from the four new fractional operators.展开更多
In this research,novel epidemic models based on fractional calculus are developed by utilizing the Caputo and Atangana-Baleanu(AB)derivatives.These models integrate vaccination effects,additional safety measures,home ...In this research,novel epidemic models based on fractional calculus are developed by utilizing the Caputo and Atangana-Baleanu(AB)derivatives.These models integrate vaccination effects,additional safety measures,home and hospital isolation,and treatment options.Fractional models are particularly significant as they provide a more comprehensive understanding of epidemic diseases and can account for non-locality and memory effects.Equilibrium points of the model are calculated,including the disease-free and endemic equilibrium points,and the basic reproduction number R0 is computed using the next-generation matrix approach.Results indicate that the epidemic becomes endemic when R0 is greater than unity,and it goes extinct when it is less than unity.The positiveness and boundedness of the solutions of model are verified.The Routh-Hurwitz technique is utilized to analyze the local stability of equilibrium points.The Lyapunov function and the LaSalle’s principle are used to demonstrate the global stability of equilibrium points.Numerical schemes are proposed,and their validity is established by comparing them to the fourth-order Runge-Kutta(RK4)method.Numerical simulations are performed using the Adams-Bashforth-Moulton predictor-corrector algorithm for the Caputo time-fractional derivative and the Toufik-Atangana numerical technique for the AB time-fractional derivative.The study looks at how the quarantine policy affected different human population groups.On the basis of these findings,a strict quarantine policy voluntarily implemented by an informed human population can help reduce the pandemic’s spread.Additionally,vaccination efforts become a crucial tool in the fight against diseases.We can greatly lower the number of susceptible people and develop a shield of immunity in the population by guaranteeing common access to vaccinations and boosting vaccination awareness.Moreover,the graphical representations of the fractional models are also developed.展开更多
A new Willis aneurysm system is proposed, which contains the Atangana-Baleanu(AB) fractional derivative.we obtain the numerical solution of the Atangana–Baleanu fractional Willis aneurysm system(ABWAS) with the AB fr...A new Willis aneurysm system is proposed, which contains the Atangana-Baleanu(AB) fractional derivative.we obtain the numerical solution of the Atangana–Baleanu fractional Willis aneurysm system(ABWAS) with the AB fractional integral and the predictor–corrector scheme.Moreover, we research the chaotic properties of ABWAS with phase diagrams and Poincare sections.The different values of pulse pressure and system order are used to evaluate and compare their effects on ABWAS.The simulations verify that the changes of pulse pressure and system order are the significant reason for ABWAS'states varying from chaotic to steady.In addition, compared with Caputo fractional WAS(FWAS),ABWAS shows less state that is chaotic.Furthermore, the results of bifurcation diagrams of blood flow damping coefficient and reciprocal heart rate show that the blood flow velocity tends to stabilize with the increase of blood flow damping coefficient or reciprocal heart rate, which is consistent with embolization therapy and drug therapy for clinical treatment of cerebral aneurysms.Finally, in view of the fact that ABWAS in chaotic state increases the possibility of rupture of cerebral aneurysms, a reasonable controller is designed to control ABWAS based on the stability theory.Compared with the control results of FWAS by the same method, the results show that the blood flow velocity in the ABWAS system varies in a smaller range.Therefore, the control effect of ABWAS is better and more stable.The new Willis aneurysm system with Atangana–Baleanu fractional derivative provides new information for the further study on treatment and control of brain aneurysms.展开更多
The present article aims to examine the heat and mass distribution in a free convection flow of electrically conducted,generalized Jeffrey nanofluid in a heated rotatory system.The flow analysis is considered in the p...The present article aims to examine the heat and mass distribution in a free convection flow of electrically conducted,generalized Jeffrey nanofluid in a heated rotatory system.The flow analysis is considered in the presence of thermal radiation and the transverse magnetic field of strength B0.The medium is porous accepting generalized Darcy’s law.The motion of the fluid is due to the cosine oscillations of the plate.Nanofluid has been formed by the uniform dispersing of the Silver nanoparticles in regular engine oil.The problem has been modeled in the form of classical partial differential equations and then generalized by replacing time derivative with Atangana–Baleanu(AB)time-fractional derivative.Upon taking the Laplace transform technique(LTT)and using physical boundary conditions,exact expressions have been obtained for momentum,energy,and concentration distributions.The impact of a number of parameters on fluid flow is shown graphically.The numerical tables have been computed for variation in the rate of heat and mass transfer with respect to rooted parameters.Finally,the classical solution is recovered by taking the fractional parameter approaching unity.It is worth noting that by adding silver nanoparticles in regular engine oil,its heat transfer rate increased by 14.59%,which will improve the life and workability of the engine.展开更多
Illicit drug use is a significant problem that causes great material and moral losses and threatens the future of the society.For this reason,illicit drug use and related crimes are the most significant criminal cases...Illicit drug use is a significant problem that causes great material and moral losses and threatens the future of the society.For this reason,illicit drug use and related crimes are the most significant criminal cases examined by scientists.This paper aims at modeling the illegal drug use using the Atangana-Baleanu fractional derivative with Mittag-Leffler kernel.Also,in this work,the existence and uniqueness of solutions of the fractional-order Illicit drug use model are discussed via Picard-Lindelöf theorem which provides successive approximations using a convergent sequence.Then the stability analysis for both disease-free and endemic equilibrium states is conducted.A numerical scheme based on the known Adams-Bashforth method is designed in fractional form to approximate the novel Atangana-Baleanu fractional operator of order 0<a≤1.Finally,numerical simulation results based on different values of fractional order,which also serve as control parameter,are presented to justify the theoretical findings.展开更多
The pivotal aim of the present investigation is to find an approximate analytical solution for the system of three fractional differential equations describing the Lakes pollution using q-homotopy analysis transform m...The pivotal aim of the present investigation is to find an approximate analytical solution for the system of three fractional differential equations describing the Lakes pollution using q-homotopy analysis transform method(q-HATM).We consider three different cases of the considered model namely,periodic input model,exponentially decaying input model,and linear input model.The considered scheme is unifications of q-homotopy analysis technique with Laplace transform(LT).To illustrate the existence and uniqueness for the projected model,we consider the fixed point hypothesis.More preciously,we scrutinized the behaviour of the obtained solution for the considered model with fractional-order,in order to elucidate the effectiveness of the proposed algorithm.Further,for the different fractional-order and parameters offered by the considered method,the physical natures have been apprehended.The obtained consequences evidence that the proposed method is very effective and highly methodical to study and examine the nature and its corresponding consequences of the system of fractional order differential equations describing the real word problems.展开更多
The solution for phytoplankton-toxic phytoplankton-zooplankton system with qhomotopy analysis transform method(q-HATM)is discussed.The projected system exemplifies three components(namely,zooplankton,toxic-phytoplankt...The solution for phytoplankton-toxic phytoplankton-zooplankton system with qhomotopy analysis transform method(q-HATM)is discussed.The projected system exemplifies three components(namely,zooplankton,toxic-phytoplankton as well as phytoplankton)and the corresponding nonlinear ordinary differential equations exemplify the zooplankton feeds on phytoplankton.The projected method is an amalgamation of q-homotopy analysis algorithm and Laplace transform and the derivative associated with the Atangana-Baleanu(AB)operator.The equilibrium points and stability have been discussed with the assistance of the Routh-Hurwitz rule in this work within the frame of generalized calculus.The fixed-point theorem is employed to present the existence and uniqueness of the attained result for the considered model,and we consider five different initial conditions for the projected system.Further,the physical nature of the achieved solution has been captured for fractional order,external force and diverse mass.The achieved consequences explicate that the proposed solution method is highly methodical,easy to implement and accurate to analyze the behavior of the nonlinear system relating to allied areas of science and technology.展开更多
In this paper,we analyze the dynamical behavior of fish farm model related to Atangana-Baleanu derivative of arbitrary order.The rnodel is constituted with the group of non-linear differential equations having nutrien...In this paper,we analyze the dynamical behavior of fish farm model related to Atangana-Baleanu derivative of arbitrary order.The rnodel is constituted with the group of non-linear differential equations having nutrients,fish and mussel.We have included discrete kind gestational delay of fish.The solution of fish farm model is determined by employing homotopy analysis transforms method(HATM).Existence of and uniqueness of solution are studied through Picard-Lindelof approach.The influence of order of new non-integer order derivative on nutrients,fish and mussel is discussed.The complete study reveals that the outer food supplies manage the behavior of the model.Moreover,to show the outcomes of the study,some numerical results are demonstrated through graphs.展开更多
In this paper, we investigate a possible applicability of the newly established fractional differentiation in the field of epidemiology. To do this, we extend the model describing the Lassa hemorrhagic fever by changi...In this paper, we investigate a possible applicability of the newly established fractional differentiation in the field of epidemiology. To do this, we extend the model describing the Lassa hemorrhagic fever by changing the derivative with the time fractional derivative for the inclusion of memory. Detailed analysis of existence and uniqueness of exact solution is presented using the Banach fixed point theorem. Finally, some numerical simulations are shown to underpin the effectiveness of the used derivative.展开更多
In this paper,we study a mathematical model of Hepatitis C Virus(HCV)infection.We present a compartmental mathematical model involving healthy hepatocytes,infected hepatocytes,non-activated dendritic cells,activated d...In this paper,we study a mathematical model of Hepatitis C Virus(HCV)infection.We present a compartmental mathematical model involving healthy hepatocytes,infected hepatocytes,non-activated dendritic cells,activated dendritic cells and cytotoxic T lymphocytes.The derivative used is of non-local fractional order and with non-singular kernel.The existence and uniqueness of the system is proven and its stability is analyzed.Then,by applying the Laplace Adomian decomposition method for the fractional derivative,we present the semi-analytical solution of the model.Finally,some numerical simulations are performed for concrete values of the parameters and several graphs are plotted to reveal the qualitative properties of the solutions.展开更多
文摘We propose a mathematical model of the coronavirus disease 2019(COVID-19)to investigate the transmission and control mechanism of the disease in the community of Nigeria.Using stability theory of differential equations,the qualitative behavior of model is studied.The pandemic indicator represented by basic reproductive number R0 is obtained from the largest eigenvalue of the next-generation matrix.Local as well as global asymptotic stability conditions for the disease-free and pandemic equilibrium are obtained which determines the conditions to stabilize the exponential spread of the disease.Further,we examined this model by using Atangana–Baleanu fractional derivative operator and existence criteria of solution for the operator is established.We consider the data of reported infection cases from April 1,2020,till April 30,2020,and parameterized the model.We have used one of the reliable and efficient method known as iterative Laplace transform to obtain numerical simulations.The impacts of various biological parameters on transmission dynamics of COVID-19 is examined.These results are based on different values of the fractional parameter and serve as a control parameter to identify the significant strategies for the control of the disease.In the end,the obtained results are demonstrated graphically to justify our theoretical findings.
文摘It is a very difficult task for the researchers to find the exact solutions to mathematical problems that contain non-linear terms in the equation.Therefore,this article aims to investigate the viscous dissipation(VD)effect on the fractional model of Jeffrey fluid over a heated vertical flat plate that suddenly moves in its own plane.Based on the Atangana-Baleanu operator,the fractional model is developed from the fractional constitutive equations.VD is responsible for the non-linear behavior in the problem.Upon taking the Laplace and Fourier sine transforms,exact expressions have been obtained for momentum and energy equations.The influence of relative parameters on fluid flow and temperature distribution is shown graphically.As special cases,and for the sake of correctness,the corresponding results for second-grade fluid and Newtonian viscous fluid are also obtained.It is interesting to note that fractional parameterαprovides more than one line as compared to the classical model.This effect represents the memory effect in the fluid which is not possible to elaborate by the classical model.It is also worth noting that the temperature profile of the generalized Jeffrey fluid rises for higher values of Eckert number which is due to the enthalpy difference of the boundary layer.
文摘In this paper,we study two fractional models in the Caputo–Fabrizio sense and Atangana–Baleanu sense,in which the effects of malaria infection on mosquito biting behavior and attractiveness of humans are considered.Using Lyapunov theory,we prove the global asymptotic stability of the unique endemic equilibrium of the integer-order model,and the fractional models,whenever the basic reproduction number R0 is greater than one.By using fixed point theory,we prove existence,and conditions of the uniqueness of solutions,as well as the stability and convergence of numerical schemes.Numerical simulations for both models,using fractional Euler method and Adams–Bashforth method,respectively,are provided to confirm the effectiveness of used approximation methods for different values of the fractional-orderγ.
文摘New atypical pneumonia caused by a virus called Coronavirus(COVID-19)appeared in Wuhan,China in December 2019.Unlike previous epidemics due to the severe acute respiratory syndrome(SARS)and the Middle East respiratory syndrome coronavirus(MERS-CoV),COVID-19 has the particularity that it is more contagious than the other previous ones.In this paper,we try to predict the COVID-19 epidemic peak in Japan with the help of real-time data from January 15 to February 29,2020 with the uses of fractional derivatives,namely,Caputo derivatives,the Caputo–Fabrizio derivatives,and Atangana–Baleanu derivatives in the Caputo sense.The fixed point theory and Picard–Lindel of approach used in this study provide the proof for the existence and uniqueness analysis of the solutions to the noninteger-order models under the investi-gations.For each fractional model,we propose a numerical scheme as well as prove its stability.Using parameter values estimated from the Japan COVID-19 epidemic real data,we perform numerical simulations to confirm the effectiveness of used approxima-tion methods by numerical simulations for different values of the fractional-orderγ,and to give the predictions of COVID-19 epidemic peaks in Japan in a specific range of time intervals.
文摘Because of the features involved with their varied kernels,differential operators relying on convolution formulations have been acknowledged as effective mathematical resources for modeling real-world issues.In this paper,we constructed a stochastic fractional framework of measles spreading mechanisms with dual medication immunization considering the exponential decay and Mittag-Leffler kernels.In this approach,the overall population was separated into five cohorts.Furthermore,the descriptive behavior of the system was investigated,including prerequisites for the positivity of solutions,invariant domain of the solution,presence and stability of equilibrium points,and sensitivity analysis.We included a stochastic element in every cohort and employed linear growth and Lipschitz criteria to show the existence and uniqueness of solutions.Several numerical simulations for various fractional orders and randomization intensities are illustrated.
基金supported by the NSFC(11971475)the Natural Science Foundation of Jiangsu Province(BK20230708)+2 种基金the Natural Science Foundation for the Universities in Jiangsu Province(23KJB110003)Geng's research was supported by the NSFC(11201041)the China Postdoctoral Science Foundation(2019M651765)。
文摘Fractional calculus has drawn more attentions of mathematicians and engineers in recent years.A lot of new fractional operators were used to handle various practical problems.In this article,we mainly study four new fractional operators,namely the CaputoFabrizio operator,the Atangana-Baleanu operator,the Sun-Hao-Zhang-Baleanu operator and the generalized Caputo type operator under the frame of the k-Prabhakar fractional integral operator.Usually,the theory of the k-Prabhakar fractional integral is regarded as a much broader than classical fractional operator.Here,we firstly give a series expansion of the k-Prabhakar fractional integral by means of the k-Riemann-Liouville integral.Then,a connection between the k-Prabhakar fractional integral and the four new fractional operators of the above mentioned was shown,respectively.In terms of the above analysis,we can obtain this a basic fact that it only needs to consider the k-Prabhakar fractional integral to cover these results from the four new fractional operators.
文摘In this research,novel epidemic models based on fractional calculus are developed by utilizing the Caputo and Atangana-Baleanu(AB)derivatives.These models integrate vaccination effects,additional safety measures,home and hospital isolation,and treatment options.Fractional models are particularly significant as they provide a more comprehensive understanding of epidemic diseases and can account for non-locality and memory effects.Equilibrium points of the model are calculated,including the disease-free and endemic equilibrium points,and the basic reproduction number R0 is computed using the next-generation matrix approach.Results indicate that the epidemic becomes endemic when R0 is greater than unity,and it goes extinct when it is less than unity.The positiveness and boundedness of the solutions of model are verified.The Routh-Hurwitz technique is utilized to analyze the local stability of equilibrium points.The Lyapunov function and the LaSalle’s principle are used to demonstrate the global stability of equilibrium points.Numerical schemes are proposed,and their validity is established by comparing them to the fourth-order Runge-Kutta(RK4)method.Numerical simulations are performed using the Adams-Bashforth-Moulton predictor-corrector algorithm for the Caputo time-fractional derivative and the Toufik-Atangana numerical technique for the AB time-fractional derivative.The study looks at how the quarantine policy affected different human population groups.On the basis of these findings,a strict quarantine policy voluntarily implemented by an informed human population can help reduce the pandemic’s spread.Additionally,vaccination efforts become a crucial tool in the fight against diseases.We can greatly lower the number of susceptible people and develop a shield of immunity in the population by guaranteeing common access to vaccinations and boosting vaccination awareness.Moreover,the graphical representations of the fractional models are also developed.
基金Project supported by the State Key Program of the National Natural Science of China(Grant No.91324201)the Fundamental Research Funds for the Central Universities of China+1 种基金the Self–determined and Innovative Research Funds of WUT,China(Grant No.2018IB017)the Natural Science Foundation of Hubei Province of China(Grant No.2014CFB865)
文摘A new Willis aneurysm system is proposed, which contains the Atangana-Baleanu(AB) fractional derivative.we obtain the numerical solution of the Atangana–Baleanu fractional Willis aneurysm system(ABWAS) with the AB fractional integral and the predictor–corrector scheme.Moreover, we research the chaotic properties of ABWAS with phase diagrams and Poincare sections.The different values of pulse pressure and system order are used to evaluate and compare their effects on ABWAS.The simulations verify that the changes of pulse pressure and system order are the significant reason for ABWAS'states varying from chaotic to steady.In addition, compared with Caputo fractional WAS(FWAS),ABWAS shows less state that is chaotic.Furthermore, the results of bifurcation diagrams of blood flow damping coefficient and reciprocal heart rate show that the blood flow velocity tends to stabilize with the increase of blood flow damping coefficient or reciprocal heart rate, which is consistent with embolization therapy and drug therapy for clinical treatment of cerebral aneurysms.Finally, in view of the fact that ABWAS in chaotic state increases the possibility of rupture of cerebral aneurysms, a reasonable controller is designed to control ABWAS based on the stability theory.Compared with the control results of FWAS by the same method, the results show that the blood flow velocity in the ABWAS system varies in a smaller range.Therefore, the control effect of ABWAS is better and more stable.The new Willis aneurysm system with Atangana–Baleanu fractional derivative provides new information for the further study on treatment and control of brain aneurysms.
文摘The present article aims to examine the heat and mass distribution in a free convection flow of electrically conducted,generalized Jeffrey nanofluid in a heated rotatory system.The flow analysis is considered in the presence of thermal radiation and the transverse magnetic field of strength B0.The medium is porous accepting generalized Darcy’s law.The motion of the fluid is due to the cosine oscillations of the plate.Nanofluid has been formed by the uniform dispersing of the Silver nanoparticles in regular engine oil.The problem has been modeled in the form of classical partial differential equations and then generalized by replacing time derivative with Atangana–Baleanu(AB)time-fractional derivative.Upon taking the Laplace transform technique(LTT)and using physical boundary conditions,exact expressions have been obtained for momentum,energy,and concentration distributions.The impact of a number of parameters on fluid flow is shown graphically.The numerical tables have been computed for variation in the rate of heat and mass transfer with respect to rooted parameters.Finally,the classical solution is recovered by taking the fractional parameter approaching unity.It is worth noting that by adding silver nanoparticles in regular engine oil,its heat transfer rate increased by 14.59%,which will improve the life and workability of the engine.
文摘Illicit drug use is a significant problem that causes great material and moral losses and threatens the future of the society.For this reason,illicit drug use and related crimes are the most significant criminal cases examined by scientists.This paper aims at modeling the illegal drug use using the Atangana-Baleanu fractional derivative with Mittag-Leffler kernel.Also,in this work,the existence and uniqueness of solutions of the fractional-order Illicit drug use model are discussed via Picard-Lindelöf theorem which provides successive approximations using a convergent sequence.Then the stability analysis for both disease-free and endemic equilibrium states is conducted.A numerical scheme based on the known Adams-Bashforth method is designed in fractional form to approximate the novel Atangana-Baleanu fractional operator of order 0<a≤1.Finally,numerical simulation results based on different values of fractional order,which also serve as control parameter,are presented to justify the theoretical findings.
文摘The pivotal aim of the present investigation is to find an approximate analytical solution for the system of three fractional differential equations describing the Lakes pollution using q-homotopy analysis transform method(q-HATM).We consider three different cases of the considered model namely,periodic input model,exponentially decaying input model,and linear input model.The considered scheme is unifications of q-homotopy analysis technique with Laplace transform(LT).To illustrate the existence and uniqueness for the projected model,we consider the fixed point hypothesis.More preciously,we scrutinized the behaviour of the obtained solution for the considered model with fractional-order,in order to elucidate the effectiveness of the proposed algorithm.Further,for the different fractional-order and parameters offered by the considered method,the physical natures have been apprehended.The obtained consequences evidence that the proposed method is very effective and highly methodical to study and examine the nature and its corresponding consequences of the system of fractional order differential equations describing the real word problems.
文摘The solution for phytoplankton-toxic phytoplankton-zooplankton system with qhomotopy analysis transform method(q-HATM)is discussed.The projected system exemplifies three components(namely,zooplankton,toxic-phytoplankton as well as phytoplankton)and the corresponding nonlinear ordinary differential equations exemplify the zooplankton feeds on phytoplankton.The projected method is an amalgamation of q-homotopy analysis algorithm and Laplace transform and the derivative associated with the Atangana-Baleanu(AB)operator.The equilibrium points and stability have been discussed with the assistance of the Routh-Hurwitz rule in this work within the frame of generalized calculus.The fixed-point theorem is employed to present the existence and uniqueness of the attained result for the considered model,and we consider five different initial conditions for the projected system.Further,the physical nature of the achieved solution has been captured for fractional order,external force and diverse mass.The achieved consequences explicate that the proposed solution method is highly methodical,easy to implement and accurate to analyze the behavior of the nonlinear system relating to allied areas of science and technology.
文摘In this paper,we analyze the dynamical behavior of fish farm model related to Atangana-Baleanu derivative of arbitrary order.The rnodel is constituted with the group of non-linear differential equations having nutrients,fish and mussel.We have included discrete kind gestational delay of fish.The solution of fish farm model is determined by employing homotopy analysis transforms method(HATM).Existence of and uniqueness of solution are studied through Picard-Lindelof approach.The influence of order of new non-integer order derivative on nutrients,fish and mussel is discussed.The complete study reveals that the outer food supplies manage the behavior of the model.Moreover,to show the outcomes of the study,some numerical results are demonstrated through graphs.
文摘In this paper, we investigate a possible applicability of the newly established fractional differentiation in the field of epidemiology. To do this, we extend the model describing the Lassa hemorrhagic fever by changing the derivative with the time fractional derivative for the inclusion of memory. Detailed analysis of existence and uniqueness of exact solution is presented using the Banach fixed point theorem. Finally, some numerical simulations are shown to underpin the effectiveness of the used derivative.
基金supported by the Agencia Estatal de Investigacin(AEI)of Spain,co-financed by the European Fund for Regional Development(FEDER)corresponding to the 2014-2020 multiyear financial framework,project PID2020-113275GB-I00Instituto de Salud Carlos II,grant COV20/00617Xunta de Galicia under grant ED431C 2019/02.
文摘In this paper,we study a mathematical model of Hepatitis C Virus(HCV)infection.We present a compartmental mathematical model involving healthy hepatocytes,infected hepatocytes,non-activated dendritic cells,activated dendritic cells and cytotoxic T lymphocytes.The derivative used is of non-local fractional order and with non-singular kernel.The existence and uniqueness of the system is proven and its stability is analyzed.Then,by applying the Laplace Adomian decomposition method for the fractional derivative,we present the semi-analytical solution of the model.Finally,some numerical simulations are performed for concrete values of the parameters and several graphs are plotted to reveal the qualitative properties of the solutions.
