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An Effcient Computational Method for differential equations of fractional Type

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Computer Modeling in Engineering & Sciences 2022年第10期 47-65页

作者： Mustafa Turkyilmazoglu Department of Mathematics Hacettepe UniversityAnkara06532Turkey Department of Medical Research China Medical University HospitalChina Medical UniversityTaichung40447Taiwan

An effective solution method of fractional ordinary and partial differential equations is proposed in the present *** standard Adomian Decomposition Method(ADM)is modified via introducing a functional term involving both a variable and a parameter.A residual approach is then adopted to identify the optimal value of the embedded parameter within the frame of L^(2) *** experiments on sample problems of open literature prove that the presented algorithm is quite accurate,more advantageous over the traditional ADM and straightforward to implement for the fractional ordinary and partial differential equations of the recent focus of mathematical *** performance of the method is further evidenced against some compared commonly used numerical techniques.

关键词： fractional differential equations Adomian decomposition method optimal data residual error

BOUNDARY VALUE METHODS FOR CA PUTO FR ACTIONAL differential equations

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Journal of Computational Mathematics 2021年第1期39卷 108-129页

作者： Yongtao Zhou Chengiian Zhang Huiru Wang School of Mathematics and Statistics Huazhong University of Science and TechnologyWuhan 430074China Hubei Key Laboratory of Engineering Modeling and Scientific Computing Huazhong University of Science and TechnologyWuhan 430074China

This paper deals with the numerical computation and analysis for Caputo fractional differential equations(CFDEs).By combining the p-order boundary value methods(B-VMs)and the m-th Lagrange interpolation,a type of exte... 详细信息

关键词： fractional differential equations Caputo derivatives Boundary value methods Local stability Unique solvability Convergence.

ON A COUPLED INTEGRO-differential SYSTEM INVOLVING MIXED fractional DERIVATIVES AND INTEGRALS OF DIFFERENT ORDERS

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Acta Mathematica Scientia 2021年第4期41卷 1366-1384页

作者： Bashir AHMAD Ravi P.AGARWAL Abrar BROOM Ahmed ALSAEDI Nonlinear Analysis and Applied Mathematics(NAAM)-Research Group Department of MathematicsFaculty of ScienceKing Abdulaziz UniversityP.O.Box 80203Jeddah 21589Saudi Arabia Department of Mathematics Texas A&M UniversityKingsvilleTexas 78363-8202USA

By applying the standard fixed point theorems,we prove the existence and uniqueness results for a system of coupled differential equations involving both left Caputo and right Riemann-Liouville fractional derivatives and mixed fractional integrals,supplemented with nonlocal coupled fractional integral boundary *** example is also constructed for the illustration of the obtained results.

关键词： fractional differential equations Caputo and Riemann-Liouville fractional derivatives systems existence fixed point theorems

A Collocation Technique via Pell-Lucas Polynomials to Solve fractional differential EquationModel for HIV/AIDS with Treatment Compartment

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Computer Modeling in Engineering & Sciences 2024年第10期141卷 281-310页

作者： Gamze Yıldırım Suayip Yüzbası Department of Mathematics Faculty of ScienceAkdeniz UniversityAntalya07058Turkey Department of Mathematics Faculty of Basic ScienceGebze Technical UniversityKocaeli41400Turkey Department of Mathematics Faculty of ScienceBartın UniversityBartın74100Turkey

In this study,a numerical method based on the Pell-Lucas polynomials(PLPs)is developed to solve the fractional order HIV/AIDS epidemic model with a treatment *** HIV/AIDS mathematical model with a treatment compartment is divided into five classes,namely,susceptible patients(S),HIV-positive individuals(I),individuals with full-blown AIDS but not receiving ARV treatment(A),individuals being treated(T),and individuals who have changed their sexual habits sufficiently(R).According to the method,by utilizing the PLPs and the collocation points,we convert the fractional order HIV/AIDS epidemic model with a treatment compartment into a nonlinear system of the algebraic ***,the error analysis is presented for the Pell-Lucas approximation *** aim of this study is to observe the behavior of five populations after 200 days when drug treatment is applied to HIV-infectious and full-blown AIDS *** demonstrate the usefulness of this method,the applications are made on the numerical example with the help of *** addition,four cases of the fractional order derivative(p=1,p=0.95,p=0.9,p=0.85)are examined in the range[0,200].Owing to applications,we figured out that the outcomes have quite decent ***,we understand that the errors decrease when the value of N *** figures in this study are created in *** outcomes indicate that the presented method is reasonably sufficient and correct.

关键词： Collocation method fractional differential equations HIV/AIDS epidemic model Pell-Lucas polynomials

EXISTENCE AND UNIQUENESS OF THE SOLUTION FOR A CLASS OF NONLINEAR fractional differential SYSTEM

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Annals of differential equations 2006年第3期22卷 467-472页

作者： Zhang Xiuyun Kou Chunhai (Dept. of Applied Math., Donghua University, Shanghai 201620)

In this paper we prove the existence and uniqueness of the solution for a class of nonlinear fractional differential system, and investigate the dependence of the solution on the orderαi.

关键词： Riemann-Liouville fractional derivative/integral fractional differential equations existence uniqueness dependence

EXISTENCE OF SOLUTIONS OF NONLINEAR fractional PANTOGRAPH equations

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Acta Mathematica Scientia 2013年第3期33卷 712-720页

作者： K. BALACHANDRAN S. KIRUTHIKA J. TRUJILLO Department of Mathematics Bharathiar University Universidad de La Laguna Departamento de Anlisis Matemtico38271 La Laguna Tenerife Spain

This article deals with the existence of solutions of nonlinear fractional pantograph equations. Such model can be considered suitable to be applied when the corresponding process occurs through strongly anomalous media. The results are obtained using fractional calculus and fixed point theorems. An example is provided to illustrate the main result obtained in this article.

关键词： fractional differential equations pantograph equations fixed point theorems

Moving Finite Element Methods for a System of Semi-Linear fractional Diffusion equations

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Advances in Applied Mathematics and Mechanics 2016年第6期8卷 911-931页

作者： Jingtang Ma Zhiqiang Zhou School of Economic Mathematics Southwestern University of Finance and EconomicsChengdu 611130China

This paper studies a system of semi-linear fractional diffusion equations which arise in competitive predator-preymodels by replacing the second-order derivatives in the spatial variables with fractional derivatives of order less than *** finite element methods are proposed to solve the system of fractional diffusion equations and the convergence rates of the methods are *** examples are carried out to confirm the theoretical *** applications in anomalous diffusive Lotka-Volterra and Michaelis-Menten-Holling predator-preymodels are studied.

关键词： Finite element methods fractional differential equations predator-preymodels

A unique computational investigation of the exact traveling wave solutions for the fractional-order Kaup-Boussinesq and generalized Hirota Satsuma coupled KdV systems arising from water waves and interaction of long waves

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Journal of Ocean Engineering and Science 2024年第5期9卷 437-453页

作者： Xiaofeng Wang Xiao-Guang Yue Mohammed K.A.Kaabar Arzu Akbulut Melike Kaplan Shenzhen University ShenzhenChina Department of Computer Science and Engineering European University CyprusNicosiaCyprus Institute of Mathematical Sciences Faculty of ScienceUniversity of MalayaKuala Lumpur 50603Malaysia Department of Mathematics and Statistics Washington State UniversityPullmanWA 99163USA Jabalia Camp United Nations Relief and Works Agency(UNRWA)Palestinian Refugee CampGaza Strip JabalyaPalestine Mathematics-Computer Department Art-Science FacultyEski¸s ehir Osmangazi UniversityEski¸s ehirTurkey Department of Computer Engineering Faculty of Engineering and ArchitectureKastamonu UniversityKastamonuTurkey

A novel technique,named auxiliary equation method,is applied in this research work for obtaining new traveling wave solutions for two interesting proposed systems:the Kaup-Boussinesq system and generalized Hirota-Satsuma coupled KdV system with beta time fractional *** solutions were obtained using MAPLE *** technique shows a great potential to be applied in solving various nonlinear fractional differential equations arising from mathematical physics and ocean *** a standard equation has not been used as an auxiliary equation for this technique,different and novel solutions are obtained via this technique.

关键词： Symbolic computation fractional differential equations Beta derivative Auxiliary equation method Solitary solutions Nonlinear equations

Ebola virus disease model with a nonlinear incidence rate and density-dependent treatment

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Infectious Disease Modelling 2024年第3期9卷 775-804页

作者： Jacques NdéKengne Calvin Tadmon Committed Mathematics Team Research Unit in Mathematics and ApplicationsDepartment of Mathematics and Computer ScienceUniversity of DschangP.O.Box 67 DschangCameroon Institute of Mathematics University of MainzStaudingerweg 955128MainzGermany

This paper studies an Ebola epidemic model with an exponential nonlinear incidence function that considers the efficacy and the behaviour *** current model also incorporates a new density-dependent treatment that catches the impact of the disease transmission on the ***,we provide a theoretical study of the nonlinear differential equations model *** precisely,we derive the effective reproduction number and,under suitable conditions,prove the stability of ***,we show that the model exhibits the phenomenon of backward-bifurcation whenever the bifurcation parameter and the reproduction number are less than *** find that the bi-stability and backward-bifurcation are not automatically connected in epidemic *** fact,when a backward-bifurcation occurs,the disease-free equilibrium may be globally ***,we use well-known standard tools to fit the model to the data reported for the 2018–2020 Kivu Ebola outbreak,and perform the sensitivity *** control Ebola epidemics,our findings recommend a combination of a rapid behaviour change and the implementation of a proper treatment strategy with a high level of ***,we propose and analyze a fractional-order Ebola epidemic model,which is an extension of the first model *** use the Caputo operator and construct the Grünwald-Letnikov nonstandard finite difference scheme,and show its advantages.

关键词： Ebola epidemic models Stability Bifurcation Density-dependent treatment Sensitivity analysis fractional differential equations Caputo fractional derivative Grünwald-letnikov nonstandard finite difference scheme