In this paper,two crossover hybrid variable-order derivatives of the cancer model are developed.Grünwald-Letnikov approximation is used to approximate the hybrid fractional and variable-order fractional operators...In this paper,two crossover hybrid variable-order derivatives of the cancer model are developed.Grünwald-Letnikov approximation is used to approximate the hybrid fractional and variable-order fractional operators.The existence,uniqueness,and stability of the proposed model are discussed.Adams Bashfourth’s fifth-step method with a hybrid variable-order fractional operator is developed to study the proposed models.Comparative studies with generalized fifth-order Runge-Kutta method are given.Numerical examples and comparative studies to verify the applicability of the used methods and to demonstrate the simplicity of these approximations are presented.We have showcased the efficiency of the proposed method and garnered robust empirical support for our theoretical findings.展开更多
This paper is concerned with the following variable-order fractional Laplacian equations , where N ≥ 1 and N > 2s(x,y) for (x,y) ∈ Ω × Ω, Ω is a bounded domain in R<sup>N</sup>, s(⋅)...This paper is concerned with the following variable-order fractional Laplacian equations , where N ≥ 1 and N > 2s(x,y) for (x,y) ∈ Ω × Ω, Ω is a bounded domain in R<sup>N</sup>, s(⋅) ∈ C (R<sup>N</sup> × R<sup>N</sup>, (0,1)), (-Δ)<sup>s(⋅)</sup> is the variable-order fractional Laplacian operator, λ, μ > 0 are two parameters, V: Ω → [0, ∞) is a continuous function, f ∈ C(Ω × R) and q ∈ C(Ω). Under some suitable conditions on f, we obtain two solutions for this problem by employing the mountain pass theorem and Ekeland’s variational principle. Our result generalizes the related ones in the literature.展开更多
In recent years,fractional-order chaotic maps have been paid more attention in publications because of the memory effect.This paper presents a novel variable-order fractional sine map(VFSM)based on the discrete fracti...In recent years,fractional-order chaotic maps have been paid more attention in publications because of the memory effect.This paper presents a novel variable-order fractional sine map(VFSM)based on the discrete fractional calculus.Specially,the order is defined as an iterative function that incorporates the current state of the system.By analyzing phase diagrams,time sequences,bifurcations,Lyapunov exponents and fuzzy entropy complexity,the dynamics of the proposed map are investigated comparing with the constant-order fractional sine map.The results reveal that the variable order has a good effect on improving the chaotic performance,and it enlarges the range of available parameter values as well as reduces non-chaotic windows.Multiple coexisting attractors also enrich the dynamics of VFSM and prove its sensitivity to initial values.Moreover,the sequence generated by the proposed map passes the statistical test for pseudorandom number and shows strong robustness to parameter estimation,which proves the potential applications in the field of information security.展开更多
In this paper,we consider numerical methods for two-sided space variable-order fractional diffusion equations(VOFDEs)with a nonlinear source term.The implicit Euler(IE)method and a shifted Grünwald(SG)scheme are ...In this paper,we consider numerical methods for two-sided space variable-order fractional diffusion equations(VOFDEs)with a nonlinear source term.The implicit Euler(IE)method and a shifted Grünwald(SG)scheme are used to approximate the temporal derivative and the space variable-order(VO)fractional derivatives,respectively,which leads to an IE-SG scheme.Since the order of the VO derivatives depends on the space and the time variables,the corresponding coefficient matrices arising from the discretization of VOFDEs are dense and without the Toeplitz-like structure.In light of the off-diagonal decay property of the coefficient matrices,we consider applying the preconditioned generalized minimum residual methods with banded preconditioners to solve the discretization systems.The eigenvalue distribution and the condition number of the preconditioned matrices are studied.Numerical results show that the proposed banded preconditioners are efficient.展开更多
The goal of this paper is to establish the boundedness of the p-adic fractional integral operator with rough kernel I_(β,Ω′)^(p)and its commutators generated by b∈Λ_(γ)(Q_(p)^(n))(0<γ<1)and the I_(β,Ω′...The goal of this paper is to establish the boundedness of the p-adic fractional integral operator with rough kernel I_(β,Ω′)^(p)and its commutators generated by b∈Λ_(γ)(Q_(p)^(n))(0<γ<1)and the I_(β,Ω′)^(p) on grand p-adic Herz spaces.展开更多
In this article,we prove the boundedness for commutators of fractional Hardy and Hardy-Littlewood-Pólya operators on grand p-adic variable Herz spaces,where the symbols of the commutators belong to Lipschitz spaces.
HIV infection continues to pose a significant global health challenge,with subSaharan Africa bearing a disproportionate burden.The replication cycle of HIV is fundamentally driven by intricate molecular interactions.T...HIV infection continues to pose a significant global health challenge,with subSaharan Africa bearing a disproportionate burden.The replication cycle of HIV is fundamentally driven by intricate molecular interactions.This study investigates the competitive biochemical interplay between reverse transcriptase(RT)and integrase(IN)enzymes,employing a fractional calculus framework to model their mutual inhibitory effects.Through the application of fixed-point theory and Picard stability analysis,the existence,uniqueness,and stability of the fractional-order system are rigorously established.The role of RT-IN enzymatic competition in influencing HIV replication dynamics is elucidated through global sensitivity analysis using Latin Hypercube Sampling.Furthermore,the model incorporates memory-dependent characteristics by examining three distinct fractional operators,namely,the Caputo,Caputo-Fabrizio,and Atangana-Baleanu operators in the Caputo sense,thereby elucidating their respective influences on system behavior.The Atangana-Baleanu operator,in particular,demonstrates an enhanced capacity to capture the complex,synergistic processes underpinning HIV progression.This research provides a critical nexus between molecular virology and applied mathematics,offering foundational insights for the advancement of more precise and targeted therapeutic strategies against HIV.展开更多
Lassa Fever(LF)is a viral hemorrhagic illness transmitted via rodents and is endemic in West Africa,causing thousands of deaths annually.This study develops a dynamic model of Lassa virus transmission,capturing the pr...Lassa Fever(LF)is a viral hemorrhagic illness transmitted via rodents and is endemic in West Africa,causing thousands of deaths annually.This study develops a dynamic model of Lassa virus transmission,capturing the progression of the disease through susceptible,exposed,infected,and recovered populations.The focus is on simulating this model using the fractional Caputo derivative,allowing both qualitative and quantitative analyses of boundedness,positivity,and solution uniqueness.Fixed-point theory and Lipschitz conditions are employed to confirm the existence and uniqueness of solutions,while Lyapunov functions establish the global stability of both disease-free and endemic equilibria.The study further examines the role of the Caputo operator by solving the generalized power-law kernel via a two-step Lagrange polynomial method.This approach offers practical advantages in handling additional data points in integral forms,though Newton polynomial-based schemes are generally more accurate and can outperform Lagrange-based Adams-Bashforth methods.Graphical simulations validate the proposed numerical approach for different fractional orders(ν)and illustrate the influence of model parameters on disease dynamics.Results indicate that increasing the fractional order accelerates the decline of Lassa fever in both human and rodent populations.Moreover,fractional-order modeling provides more nuanced insights than traditional integer-order models,suggesting potential improvements for medical intervention strategies.The study demonstrates that carefully chosen fractional orders can optimize convergence and enhance the predictive capacity of Lassa fever models,offering a promising direction for future research in epidemiological modeling.展开更多
Background There is still limited data on predictive value of coronary computed tomography angiography(CCTA)–derived fractional flow reserve(CT-FFR) for long term outcomes. We examined the long-term prognostic value ...Background There is still limited data on predictive value of coronary computed tomography angiography(CCTA)–derived fractional flow reserve(CT-FFR) for long term outcomes. We examined the long-term prognostic value of CT-FFR combined with CCTA–defined atherosclerotic extent in diabetic patients with coronary artery disease(CAD).Methods A retrospective pooled analysis of individual patient data was performed. Deep-learning-based vessel-specific CTFFR was calculated. All patients enrolled were followed-up for at least 5 years. Predictive abilities for major adverse cardiac events(MACE) were compared among three models(model 1), constructed using clinical variables;model 2, model 1+CCTA–derived atherosclerotic extent(Leiden risk score);and model 3, model 2+CT-FFR.Results A total of 480 diabetic patients [median age, 61(55–66) years;52.9% men] were included. During a median follow-up time of 2197(2126–2355) days, 55 patients(11.5%) experienced MACE. In multivariate-adjusted Cox models, Leiden risk score(HR: 1.06;95% CI: 1.01–1.11;P = 0.013) and CT-FFR ≤ 0.80(HR: 6.54;95% CI: 3.18–13.45;P < 0.001) were the independent predictors. The discriminant ability was higher in model 2 than in model 1(C-index, 0.75 vs. 0.63;P < 0.001) and was further promoted by adding CT-FFR to model 3(C-index, 0.81 vs. 0.75;P = 0.002). Net reclassification improvement(NRI) was 0.19(P = 0.009) for model 2 beyond model 1. Of note, adding CT-FFR to model 3 also exhibited significantly improved reclassification compared with model 2(NRI = 0.14;P = 0.011).Conclusion In diabetic patients with CAD, CT-FFR provides robust and incremental prognostic information for predicting longterm outcomes. The combined model exhibits improved prediction abilities, which is beneficial for risk stratification.展开更多
Lithium(Li)is an‘emerging'environmental pollutant,especially in soil,which is a great concern because it can endanger human health through the food chain.Compared with traditional chemical analyses,hyperspectral ...Lithium(Li)is an‘emerging'environmental pollutant,especially in soil,which is a great concern because it can endanger human health through the food chain.Compared with traditional chemical analyses,hyperspectral techniques have achieved many exciting results in soil metal monitoring due to their advantages of being fast and non-destructive.However,insufficient attention has been paid to lithium in soil,and the feasibility of its estimation using hyperspectral techniques needs to be investigated.We studied 97 soil samples from claytype lithium mines in the Ertanggou area of the East Tianshan Mountains of Xinjiang to explore the effects of spectral resolution,fractional order derivatives(FOD),and characteristic band selection on the estimation accuracy of clay Li content,to obtain a fast and effective method for estimating clay Li content.Finally,we developed a new method for rapid and nondestructive estimation of soil lithium content.We have obtained some important results from the study.Spectral resolution exerts a significant impact on model performance,and its reduction usually leads to a decline in model performance.For the full band,the models constructed with low-order derivatives were superior to those with high-order derivatives,and the best model was obtained at the 0.4-order derivative(coefficient of determination(R^(2))and relative predictive deviation(RPD)of 0.777 and 2.118,respectively).In the characteristic bands,the lower order is sensitive to the visible-near-infrared range,and the higher order is sensitive to the short-wave infrared range,and the model constructed with the higher-order derivatives outperforms the lower-order derivatives.In this study,the combination of FOD and Random Forest(RF)can significantly improve the model performance,with R^(2),Relative Root Mean Squared Error(RRMSE),and RPD being 0.849,1.526,and 2.574,respectively.Therefore,this research provides a theoretical basis and technical reference for imaging hyperspectral exploration of anomalous areas of clay-type Li resources.展开更多
In this paper,we study a class of Linear Fractional Programming on a nonempty bounded set,called the Problem(LFP),and design a branch and bound algorithm to find the global optimal solution of the problem(LFP).First,w...In this paper,we study a class of Linear Fractional Programming on a nonempty bounded set,called the Problem(LFP),and design a branch and bound algorithm to find the global optimal solution of the problem(LFP).First,we convert the problem(LFP)to the equivalent problem(EP2).Secondly,by applying the linear relaxation technique to the problem(EP2),the linear relaxation programming problem(LRP2Y)was obtained.Then,the overall framework of the algorithm is given,and the convergence and complexity of the algorithm are analyzed.Finally,experimental results are listed to illustrate the effectiveness of the algorithm.展开更多
We investigate the constrained fractional Choquard equation■where m>0,N>2s with s∈(0,1)being the order of the fractional Laplacian operator and I_(α)forα∈(0,N)denotes the Riesz potential.The parameterμ∈ℝa...We investigate the constrained fractional Choquard equation■where m>0,N>2s with s∈(0,1)being the order of the fractional Laplacian operator and I_(α)forα∈(0,N)denotes the Riesz potential.The parameterμ∈ℝappears as a Lagrange multiplier.By imposing general mass-supercritical conditions on F,we confirm the existence of normalized solutions that characterize the global minimizer on the Pohozaev manifold.Our proof does not depend on the assumption that all weak solutions satisfy the Pohozaev identity,a challenge that remains unsolved for this doubly nonlocal equation.展开更多
The fractional quantum Hall effect remains a captivating area in condensed matter physics,characterized by strongly correlated topological order,which manifests as fractionalized excitations and anyonic statistics.Num...The fractional quantum Hall effect remains a captivating area in condensed matter physics,characterized by strongly correlated topological order,which manifests as fractionalized excitations and anyonic statistics.Numerical simulations,such as exact diagonalization,density matrix renormalization groups,matrix product states,and Monte Carlo methods are essential for examining the properties of strongly correlated systems.Recently,density functional theory has been employed in this field within the framework of composite fermion theory.This paper systematically evaluates how density functional theory approaches have addressed fundamental challenges in fractional quantum Hall systems,including ground state and low-energy excitations.Special attention is given to the insights provided by density functional theory regarding composite fermion behavior,edge effects,and the nature of fractional charge and magnetoroton excitations.The discussion critically examines both the advantages and limitations of these approaches,while highlighting the productive interplay between numerical simulations and theoretical models.Future directions are explored,particularly the promising potential of time-dependent density functional theory for modeling non-equilibrium dynamics in quantum Hall systems.展开更多
This paper introduces a novel fractional-order model based on the Caputo-Fabrizio(CF)derivative for analyzing computer virus propagation in networked environments.The model partitions the computer population into four...This paper introduces a novel fractional-order model based on the Caputo-Fabrizio(CF)derivative for analyzing computer virus propagation in networked environments.The model partitions the computer population into four compartments:susceptible,latently infected,breaking-out,and antivirus-capable systems.By employing the CF derivative—which uses a nonsingular exponential kernel—the framework effectively captures memory-dependent and nonlocal characteristics intrinsic to cyber systems,aspects inadequately represented by traditional integer-order models.Under Lipschitz continuity and boundedness assumptions,the existence and uniqueness of solutions are rigorously established via fixed-point theory.We develop a tailored two-step Adams-Bashforth numerical scheme for the CF framework and prove its second-order accuracy.Extensive numerical simulations across various fractional orders reveal that memory effects significantly influence virus transmission and control dynamics;smaller fractional orders produce more pronounced memory effects,delaying both infection spread and antivirus activation.Further theoretical analysis,including Hyers-Ulam stability and sensitivity assessments,reinforces the model’s robustness and identifies key parameters governing virus dynamics.The study also extends the framework to incorporate stochastic effects through a stochastic CF formulation.These results underscore fractional-order modeling as a powerful analytical tool for developing robust and effective cybersecurity strategies.展开更多
In this paper,we first give a sufficient condition for a graph being fractional ID-[a,b]-factor-critical covered in terms of its independence number and minimum degree,which partially answers the problem posed by Sizh...In this paper,we first give a sufficient condition for a graph being fractional ID-[a,b]-factor-critical covered in terms of its independence number and minimum degree,which partially answers the problem posed by Sizhong Zhou,Hongxia Liu and Yang Xu(2022).Then,an A_(α)-spectral condition is given to ensure that G is a fractional ID-[a,b]-factor-critical covered graph and an(a,b,k)-factor-critical graph,respectively.In fact,(a,b,k)-factor-critical graph is a graph which has an[a,b]-factor for k=0.Thus,these above results extend the results of Jia Wei and Shenggui Zhang(2023)and Ao Fan,Ruifang Liu and Guoyan Ao(2023)in some sense.展开更多
In this paper,we first prove the existence and uniqueness theorem of the solution of nonlinear variable-order fractional stochastic differential equations(VFSDEs).We futher constructe the Euler-Maruyama method to solv...In this paper,we first prove the existence and uniqueness theorem of the solution of nonlinear variable-order fractional stochastic differential equations(VFSDEs).We futher constructe the Euler-Maruyama method to solve the equations and prove the convergence in mean and the strong convergence of the method.In particular,when the fractional order is no longer varying,the conclusions obtained are consistent with the relevant conclusions in the existing literature.Finally,the numerical experiments at the end of the article verify the correctness of the theoretical results obtained.展开更多
In this paper, we study the solutions for variable-order time-fractional diffusion equations. A three-point combined compact difference (CCD) method is used to discretize the spatial variables to achieve sixth-order a...In this paper, we study the solutions for variable-order time-fractional diffusion equations. A three-point combined compact difference (CCD) method is used to discretize the spatial variables to achieve sixth-order accuracy, while the exponential-sum-approximation (ESA) is used to approximate the variable-order Caputo fractional derivative in the temporal direction, and a novel spatial sixth-order hybrid ESA-CCD method is implemented successfully. Finally, the accuracy of the proposed method is verified by numerical experiments.展开更多
The aim of this paper is to develop a fully discrete local discontinuous Galerkin method to solve a class of variable-order fractional diffusion problems.The scheme is discretized by a weighted-shifted Grünwald f...The aim of this paper is to develop a fully discrete local discontinuous Galerkin method to solve a class of variable-order fractional diffusion problems.The scheme is discretized by a weighted-shifted Grünwald formula in the temporal discretization and a local discontinuous Galerkin method in the spatial direction.The stability and the L^(2)-convergence of the scheme are proved for all variable-orderα(t)∈(0,1).The proposed method is of accuracy-order O(τ^(3)+h^(k+1)),whereτ,h,and k are the temporal step size,the spatial step size,and the degree of piecewise P^(k)polynomials,respectively.Some numerical tests are provided to illustrate the accuracy and the capability of the scheme.展开更多
Nonlinear fractional differential equations provide suitable models to describe real-world phenomena and many fractional derivatives are varying with time and space.The present study considers the advanced and broad s...Nonlinear fractional differential equations provide suitable models to describe real-world phenomena and many fractional derivatives are varying with time and space.The present study considers the advanced and broad spectrum of the nonlinear(NL)variable-order fractional differential equation(VO-FDE)in sense of VO Caputo fractional derivative(CFD)to describe the physical models.The VO-FDE transforms into an ordinary differential equation(ODE)and then solving by the modified(G/G)-expansion method.For ac-curacy,the space-time VO fractional Korteweg-de Vries(KdV)equation is solved by the proposed method and obtained some new types of periodic wave,singular,and Kink exact solutions.The newly obtained solutions confirmed that the proposed method is well-ordered and capable implement to find a class of NL-VO equations.The VO non-integer performance of the solutions is studied broadly by using 2D and 3D graphical representation.The results revealed that the NL VO-FDEs are highly active,functional and convenient in explaining the problems in scientific physics.展开更多
In this paper,we present local functional law of the iterated logarithm for Cs?rg?-Révész type increments of fractional Brownian motion.The results obtained extend works of Gantert[Ann.Probab.,1993,21(2):104...In this paper,we present local functional law of the iterated logarithm for Cs?rg?-Révész type increments of fractional Brownian motion.The results obtained extend works of Gantert[Ann.Probab.,1993,21(2):1045-1049]and Monrad and Rootzén[Probab.Theory Related Fields,1995,101(2):173-192].展开更多
文摘In this paper,two crossover hybrid variable-order derivatives of the cancer model are developed.Grünwald-Letnikov approximation is used to approximate the hybrid fractional and variable-order fractional operators.The existence,uniqueness,and stability of the proposed model are discussed.Adams Bashfourth’s fifth-step method with a hybrid variable-order fractional operator is developed to study the proposed models.Comparative studies with generalized fifth-order Runge-Kutta method are given.Numerical examples and comparative studies to verify the applicability of the used methods and to demonstrate the simplicity of these approximations are presented.We have showcased the efficiency of the proposed method and garnered robust empirical support for our theoretical findings.
文摘This paper is concerned with the following variable-order fractional Laplacian equations , where N ≥ 1 and N > 2s(x,y) for (x,y) ∈ Ω × Ω, Ω is a bounded domain in R<sup>N</sup>, s(⋅) ∈ C (R<sup>N</sup> × R<sup>N</sup>, (0,1)), (-Δ)<sup>s(⋅)</sup> is the variable-order fractional Laplacian operator, λ, μ > 0 are two parameters, V: Ω → [0, ∞) is a continuous function, f ∈ C(Ω × R) and q ∈ C(Ω). Under some suitable conditions on f, we obtain two solutions for this problem by employing the mountain pass theorem and Ekeland’s variational principle. Our result generalizes the related ones in the literature.
基金Project supported by the National Natural Science Foundation of China(Grant Nos.62071496,61901530,and 62061008)the Natural Science Foundation of Hunan Province of China(Grant No.2020JJ5767).
文摘In recent years,fractional-order chaotic maps have been paid more attention in publications because of the memory effect.This paper presents a novel variable-order fractional sine map(VFSM)based on the discrete fractional calculus.Specially,the order is defined as an iterative function that incorporates the current state of the system.By analyzing phase diagrams,time sequences,bifurcations,Lyapunov exponents and fuzzy entropy complexity,the dynamics of the proposed map are investigated comparing with the constant-order fractional sine map.The results reveal that the variable order has a good effect on improving the chaotic performance,and it enlarges the range of available parameter values as well as reduces non-chaotic windows.Multiple coexisting attractors also enrich the dynamics of VFSM and prove its sensitivity to initial values.Moreover,the sequence generated by the proposed map passes the statistical test for pseudorandom number and shows strong robustness to parameter estimation,which proves the potential applications in the field of information security.
文摘In this paper,we consider numerical methods for two-sided space variable-order fractional diffusion equations(VOFDEs)with a nonlinear source term.The implicit Euler(IE)method and a shifted Grünwald(SG)scheme are used to approximate the temporal derivative and the space variable-order(VO)fractional derivatives,respectively,which leads to an IE-SG scheme.Since the order of the VO derivatives depends on the space and the time variables,the corresponding coefficient matrices arising from the discretization of VOFDEs are dense and without the Toeplitz-like structure.In light of the off-diagonal decay property of the coefficient matrices,we consider applying the preconditioned generalized minimum residual methods with banded preconditioners to solve the discretization systems.The eigenvalue distribution and the condition number of the preconditioned matrices are studied.Numerical results show that the proposed banded preconditioners are efficient.
基金Supported by Natural Science Foundation of China(12461021)。
文摘The goal of this paper is to establish the boundedness of the p-adic fractional integral operator with rough kernel I_(β,Ω′)^(p)and its commutators generated by b∈Λ_(γ)(Q_(p)^(n))(0<γ<1)and the I_(β,Ω′)^(p) on grand p-adic Herz spaces.
基金Supported by Chizhou University High Level Talent Research Start up Fund (No.CZ2025YJRC52)。
文摘In this article,we prove the boundedness for commutators of fractional Hardy and Hardy-Littlewood-Pólya operators on grand p-adic variable Herz spaces,where the symbols of the commutators belong to Lipschitz spaces.
基金Supported by the DST FIST Programme(SR/FST/MS-II/2021/101(C))UGC-JRF(21161010788)+1 种基金supported by NSFC(11831003,12171111)SFC(KZ202110005011)。
文摘HIV infection continues to pose a significant global health challenge,with subSaharan Africa bearing a disproportionate burden.The replication cycle of HIV is fundamentally driven by intricate molecular interactions.This study investigates the competitive biochemical interplay between reverse transcriptase(RT)and integrase(IN)enzymes,employing a fractional calculus framework to model their mutual inhibitory effects.Through the application of fixed-point theory and Picard stability analysis,the existence,uniqueness,and stability of the fractional-order system are rigorously established.The role of RT-IN enzymatic competition in influencing HIV replication dynamics is elucidated through global sensitivity analysis using Latin Hypercube Sampling.Furthermore,the model incorporates memory-dependent characteristics by examining three distinct fractional operators,namely,the Caputo,Caputo-Fabrizio,and Atangana-Baleanu operators in the Caputo sense,thereby elucidating their respective influences on system behavior.The Atangana-Baleanu operator,in particular,demonstrates an enhanced capacity to capture the complex,synergistic processes underpinning HIV progression.This research provides a critical nexus between molecular virology and applied mathematics,offering foundational insights for the advancement of more precise and targeted therapeutic strategies against HIV.
文摘Lassa Fever(LF)is a viral hemorrhagic illness transmitted via rodents and is endemic in West Africa,causing thousands of deaths annually.This study develops a dynamic model of Lassa virus transmission,capturing the progression of the disease through susceptible,exposed,infected,and recovered populations.The focus is on simulating this model using the fractional Caputo derivative,allowing both qualitative and quantitative analyses of boundedness,positivity,and solution uniqueness.Fixed-point theory and Lipschitz conditions are employed to confirm the existence and uniqueness of solutions,while Lyapunov functions establish the global stability of both disease-free and endemic equilibria.The study further examines the role of the Caputo operator by solving the generalized power-law kernel via a two-step Lagrange polynomial method.This approach offers practical advantages in handling additional data points in integral forms,though Newton polynomial-based schemes are generally more accurate and can outperform Lagrange-based Adams-Bashforth methods.Graphical simulations validate the proposed numerical approach for different fractional orders(ν)and illustrate the influence of model parameters on disease dynamics.Results indicate that increasing the fractional order accelerates the decline of Lassa fever in both human and rodent populations.Moreover,fractional-order modeling provides more nuanced insights than traditional integer-order models,suggesting potential improvements for medical intervention strategies.The study demonstrates that carefully chosen fractional orders can optimize convergence and enhance the predictive capacity of Lassa fever models,offering a promising direction for future research in epidemiological modeling.
文摘Background There is still limited data on predictive value of coronary computed tomography angiography(CCTA)–derived fractional flow reserve(CT-FFR) for long term outcomes. We examined the long-term prognostic value of CT-FFR combined with CCTA–defined atherosclerotic extent in diabetic patients with coronary artery disease(CAD).Methods A retrospective pooled analysis of individual patient data was performed. Deep-learning-based vessel-specific CTFFR was calculated. All patients enrolled were followed-up for at least 5 years. Predictive abilities for major adverse cardiac events(MACE) were compared among three models(model 1), constructed using clinical variables;model 2, model 1+CCTA–derived atherosclerotic extent(Leiden risk score);and model 3, model 2+CT-FFR.Results A total of 480 diabetic patients [median age, 61(55–66) years;52.9% men] were included. During a median follow-up time of 2197(2126–2355) days, 55 patients(11.5%) experienced MACE. In multivariate-adjusted Cox models, Leiden risk score(HR: 1.06;95% CI: 1.01–1.11;P = 0.013) and CT-FFR ≤ 0.80(HR: 6.54;95% CI: 3.18–13.45;P < 0.001) were the independent predictors. The discriminant ability was higher in model 2 than in model 1(C-index, 0.75 vs. 0.63;P < 0.001) and was further promoted by adding CT-FFR to model 3(C-index, 0.81 vs. 0.75;P = 0.002). Net reclassification improvement(NRI) was 0.19(P = 0.009) for model 2 beyond model 1. Of note, adding CT-FFR to model 3 also exhibited significantly improved reclassification compared with model 2(NRI = 0.14;P = 0.011).Conclusion In diabetic patients with CAD, CT-FFR provides robust and incremental prognostic information for predicting longterm outcomes. The combined model exhibits improved prediction abilities, which is beneficial for risk stratification.
基金Sponsored the National Natural Science Foundation of China(42502088)the National Major Science and Technology Project of China(2025ZD1007504-1)+2 种基金the Special Research Fund of Natural Science(Special Post)of Guizhou University(X202402)the Guizhou Provincial Science and Technology Projects(QKHJC[2024]youth 153)the Xinjiang Uygur Autonomous Region Natural Science Foundation(2024D01A147)。
文摘Lithium(Li)is an‘emerging'environmental pollutant,especially in soil,which is a great concern because it can endanger human health through the food chain.Compared with traditional chemical analyses,hyperspectral techniques have achieved many exciting results in soil metal monitoring due to their advantages of being fast and non-destructive.However,insufficient attention has been paid to lithium in soil,and the feasibility of its estimation using hyperspectral techniques needs to be investigated.We studied 97 soil samples from claytype lithium mines in the Ertanggou area of the East Tianshan Mountains of Xinjiang to explore the effects of spectral resolution,fractional order derivatives(FOD),and characteristic band selection on the estimation accuracy of clay Li content,to obtain a fast and effective method for estimating clay Li content.Finally,we developed a new method for rapid and nondestructive estimation of soil lithium content.We have obtained some important results from the study.Spectral resolution exerts a significant impact on model performance,and its reduction usually leads to a decline in model performance.For the full band,the models constructed with low-order derivatives were superior to those with high-order derivatives,and the best model was obtained at the 0.4-order derivative(coefficient of determination(R^(2))and relative predictive deviation(RPD)of 0.777 and 2.118,respectively).In the characteristic bands,the lower order is sensitive to the visible-near-infrared range,and the higher order is sensitive to the short-wave infrared range,and the model constructed with the higher-order derivatives outperforms the lower-order derivatives.In this study,the combination of FOD and Random Forest(RF)can significantly improve the model performance,with R^(2),Relative Root Mean Squared Error(RRMSE),and RPD being 0.849,1.526,and 2.574,respectively.Therefore,this research provides a theoretical basis and technical reference for imaging hyperspectral exploration of anomalous areas of clay-type Li resources.
基金Supported by the National Natural Science Foundation of China(Grant Nos.12571317 and 12071133).
文摘In this paper,we study a class of Linear Fractional Programming on a nonempty bounded set,called the Problem(LFP),and design a branch and bound algorithm to find the global optimal solution of the problem(LFP).First,we convert the problem(LFP)to the equivalent problem(EP2).Secondly,by applying the linear relaxation technique to the problem(EP2),the linear relaxation programming problem(LRP2Y)was obtained.Then,the overall framework of the algorithm is given,and the convergence and complexity of the algorithm are analyzed.Finally,experimental results are listed to illustrate the effectiveness of the algorithm.
基金supported by the Guangdong Basic and Applied Basic Research Foundation(2022A1515012138)the NSFC(12271436,12371119)supported by the Natural Science Basic Research Program of Shaanxi(2022JC-04).
文摘We investigate the constrained fractional Choquard equation■where m>0,N>2s with s∈(0,1)being the order of the fractional Laplacian operator and I_(α)forα∈(0,N)denotes the Riesz potential.The parameterμ∈ℝappears as a Lagrange multiplier.By imposing general mass-supercritical conditions on F,we confirm the existence of normalized solutions that characterize the global minimizer on the Pohozaev manifold.Our proof does not depend on the assumption that all weak solutions satisfy the Pohozaev identity,a challenge that remains unsolved for this doubly nonlocal equation.
基金supported by National Natural Science Foundation of China under Grant Nos.12474140 and 12347101supported by National Natural Science Foundation of China under Grant No.12204432+1 种基金supported by the graduate research and innovation foundation of Chongqing,China under Grant No.CYB25066the inaugural Doctoral Student Special Project of the China Association for Science and Technology Young Talents Lifting Program(2024)。
文摘The fractional quantum Hall effect remains a captivating area in condensed matter physics,characterized by strongly correlated topological order,which manifests as fractionalized excitations and anyonic statistics.Numerical simulations,such as exact diagonalization,density matrix renormalization groups,matrix product states,and Monte Carlo methods are essential for examining the properties of strongly correlated systems.Recently,density functional theory has been employed in this field within the framework of composite fermion theory.This paper systematically evaluates how density functional theory approaches have addressed fundamental challenges in fractional quantum Hall systems,including ground state and low-energy excitations.Special attention is given to the insights provided by density functional theory regarding composite fermion behavior,edge effects,and the nature of fractional charge and magnetoroton excitations.The discussion critically examines both the advantages and limitations of these approaches,while highlighting the productive interplay between numerical simulations and theoretical models.Future directions are explored,particularly the promising potential of time-dependent density functional theory for modeling non-equilibrium dynamics in quantum Hall systems.
基金supported and funded by the Deanship of Scientific Research at Imam Mohammad Ibn Saud Islamic University(IMSIU)(grant number IMSIU-DDRSP2601).
文摘This paper introduces a novel fractional-order model based on the Caputo-Fabrizio(CF)derivative for analyzing computer virus propagation in networked environments.The model partitions the computer population into four compartments:susceptible,latently infected,breaking-out,and antivirus-capable systems.By employing the CF derivative—which uses a nonsingular exponential kernel—the framework effectively captures memory-dependent and nonlocal characteristics intrinsic to cyber systems,aspects inadequately represented by traditional integer-order models.Under Lipschitz continuity and boundedness assumptions,the existence and uniqueness of solutions are rigorously established via fixed-point theory.We develop a tailored two-step Adams-Bashforth numerical scheme for the CF framework and prove its second-order accuracy.Extensive numerical simulations across various fractional orders reveal that memory effects significantly influence virus transmission and control dynamics;smaller fractional orders produce more pronounced memory effects,delaying both infection spread and antivirus activation.Further theoretical analysis,including Hyers-Ulam stability and sensitivity assessments,reinforces the model’s robustness and identifies key parameters governing virus dynamics.The study also extends the framework to incorporate stochastic effects through a stochastic CF formulation.These results underscore fractional-order modeling as a powerful analytical tool for developing robust and effective cybersecurity strategies.
基金Supported by the National Natural Science Foundation of China(Grant Nos.11961041,12261055)the Key Project of Natural Science Foundation of Gansu Province(Grant No.24JRRA222)the Foundation for Innovative Fundamental Research Group Project of Gansu Province(Grant No.25JRRA805).
文摘In this paper,we first give a sufficient condition for a graph being fractional ID-[a,b]-factor-critical covered in terms of its independence number and minimum degree,which partially answers the problem posed by Sizhong Zhou,Hongxia Liu and Yang Xu(2022).Then,an A_(α)-spectral condition is given to ensure that G is a fractional ID-[a,b]-factor-critical covered graph and an(a,b,k)-factor-critical graph,respectively.In fact,(a,b,k)-factor-critical graph is a graph which has an[a,b]-factor for k=0.Thus,these above results extend the results of Jia Wei and Shenggui Zhang(2023)and Ao Fan,Ruifang Liu and Guoyan Ao(2023)in some sense.
基金supported by the National Natural Science Foundation of China(No.12071403)the Scientific Research Foundation of Hunan Provincial Education Department of China(No.18A049).
文摘In this paper,we first prove the existence and uniqueness theorem of the solution of nonlinear variable-order fractional stochastic differential equations(VFSDEs).We futher constructe the Euler-Maruyama method to solve the equations and prove the convergence in mean and the strong convergence of the method.In particular,when the fractional order is no longer varying,the conclusions obtained are consistent with the relevant conclusions in the existing literature.Finally,the numerical experiments at the end of the article verify the correctness of the theoretical results obtained.
文摘In this paper, we study the solutions for variable-order time-fractional diffusion equations. A three-point combined compact difference (CCD) method is used to discretize the spatial variables to achieve sixth-order accuracy, while the exponential-sum-approximation (ESA) is used to approximate the variable-order Caputo fractional derivative in the temporal direction, and a novel spatial sixth-order hybrid ESA-CCD method is implemented successfully. Finally, the accuracy of the proposed method is verified by numerical experiments.
基金supported by the Fundamental Research Funds for the Henan Provincial Colleges and Universities in Henan University of Technology(2018RCJH10)the Training Plan of Young Backbone Teachers in Henan University of Technology(21420049)+2 种基金the Training Plan of Young Backbone Teachers in Colleges and Universities of Henan Province(2019GGJS094)the innovative Funds Plan of Henan University of Technology,Foundation of Henan Educational Committee(19A110005)the National Natural Science Foundation of China(11861068).
文摘The aim of this paper is to develop a fully discrete local discontinuous Galerkin method to solve a class of variable-order fractional diffusion problems.The scheme is discretized by a weighted-shifted Grünwald formula in the temporal discretization and a local discontinuous Galerkin method in the spatial direction.The stability and the L^(2)-convergence of the scheme are proved for all variable-orderα(t)∈(0,1).The proposed method is of accuracy-order O(τ^(3)+h^(k+1)),whereτ,h,and k are the temporal step size,the spatial step size,and the degree of piecewise P^(k)polynomials,respectively.Some numerical tests are provided to illustrate the accuracy and the capability of the scheme.
文摘Nonlinear fractional differential equations provide suitable models to describe real-world phenomena and many fractional derivatives are varying with time and space.The present study considers the advanced and broad spectrum of the nonlinear(NL)variable-order fractional differential equation(VO-FDE)in sense of VO Caputo fractional derivative(CFD)to describe the physical models.The VO-FDE transforms into an ordinary differential equation(ODE)and then solving by the modified(G/G)-expansion method.For ac-curacy,the space-time VO fractional Korteweg-de Vries(KdV)equation is solved by the proposed method and obtained some new types of periodic wave,singular,and Kink exact solutions.The newly obtained solutions confirmed that the proposed method is well-ordered and capable implement to find a class of NL-VO equations.The VO non-integer performance of the solutions is studied broadly by using 2D and 3D graphical representation.The results revealed that the NL VO-FDEs are highly active,functional and convenient in explaining the problems in scientific physics.
基金Supported by NSFC(Nos.11661025,12161024)Natural Science Foundation of Guangxi(Nos.2020GXNSFAA159118,2021GXNSFAA196045)+2 种基金Guangxi Science and Technology Project(No.Guike AD20297006)Training Program for 1000 Young and Middle-aged Cadre Teachers in Universities of GuangxiNational College Student's Innovation and Entrepreneurship Training Program(No.202110595049)。
文摘In this paper,we present local functional law of the iterated logarithm for Cs?rg?-Révész type increments of fractional Brownian motion.The results obtained extend works of Gantert[Ann.Probab.,1993,21(2):1045-1049]and Monrad and Rootzén[Probab.Theory Related Fields,1995,101(2):173-192].
