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Multiple Solutions for a Class of Singular Boundary Value Problems of Hadamard Fractional Differential Systems with p-Laplacian Operator
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作者 Chen Wang Yansheng Liu 《Journal of Applied Mathematics and Physics》 2024年第9期3114-3134,共21页
This paper discusses the existence and multiplicity of positive solutions for a class of singular boundary value problems of Hadamard fractional differential systems involving the p-Laplacian operator. First, for the ... This paper discusses the existence and multiplicity of positive solutions for a class of singular boundary value problems of Hadamard fractional differential systems involving the p-Laplacian operator. First, for the sake of overcoming the singularity, sequences of approximate solutions to the boundary value problem are obtained by applying the fixed point index theory on the cone. Next, it is demonstrated that these sequences of approximate solutions are uniformly bounded and equicontinuous. The main results are then established through the Ascoli-Arzelà theorem. Ultimately, an instance is worked out to test and verify the validity of the main results. 展开更多
关键词 Multiple Solutions Fixed Point Index Theory nonlinear fractional differential systems Hadamard fractional Derivative
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Existence Results for Systems of Nonlinear Caputo Fractional Differential Equations
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作者 Faten Toumi 《Applied Mathematics》 2023年第3期182-195,共14页
We aim, in this work, to demonstrate the existence of minimal and maximal coupled quasi-solutions for nonlinear Caputo fractional differential systems with order q ∈ (1,2). Our approach is based on mixed monotone ite... We aim, in this work, to demonstrate the existence of minimal and maximal coupled quasi-solutions for nonlinear Caputo fractional differential systems with order q ∈ (1,2). Our approach is based on mixed monotone iterative techniques developed under the concept of lower and upper quasi-solutions. Our results extend those obtained for ordinary differential equations and fractional ones. 展开更多
关键词 Mixed Quasi-Monotone Property Coupled Lower and Upper Solutions Mon-otone Method nonlinear fractional differential system
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Solving Fractional Differential Equations via Fixed Points of Chatterjea Maps
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作者 Nawab Hussain Saud M.Alsulami Hind Alamri 《Computer Modeling in Engineering & Sciences》 SCIE EI 2023年第6期2617-2648,共32页
In this paper,we present the existence and uniqueness of fixed points and common fixed points for Reich and Chatterjea pairs of self-maps in complete metric spaces.Furthermore,we study fixed point theorems for Reich a... In this paper,we present the existence and uniqueness of fixed points and common fixed points for Reich and Chatterjea pairs of self-maps in complete metric spaces.Furthermore,we study fixed point theorems for Reich and Chatterjea nonexpansive mappings in a Banach space using the Krasnoselskii-Ishikawa iteration method associated withSλand consider some applications of our results to prove the existence of solutions for nonlinear integral and nonlinear fractional differential equations.We also establish certain interesting examples to illustrate the usability of our results. 展开更多
关键词 Common fixed points Reich and Chatterjea mappings Krasnoselskii-Ishikawa iteration complete metric space Banach space integral equation nonlinear fractional differential equation
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FIXED POINTS OF α-TYPE F-CONTRACTIVE MAPPINGS WITH AN APPLICATION TO NONLINEAR FRACTIONAL DIFFERENTIAL EQUATION 被引量:3
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作者 Dhananjay GOPAL Mujahid ABBAS +1 位作者 Deepesh Kumar PATEL Calogero VETRO 《Acta Mathematica Scientia》 SCIE CSCD 2016年第3期957-970,共14页
In this paper, we introduce new concepts of a-type F-contractive mappings which are essentially weaker than the class of F-contractive mappings given in [21, 22] and different from a-GF-contractions given in [8]. Then... In this paper, we introduce new concepts of a-type F-contractive mappings which are essentially weaker than the class of F-contractive mappings given in [21, 22] and different from a-GF-contractions given in [8]. Then, sufficient conditions for the existence and uniqueness of fixed point are established for these new types of contractive mappings, in the setting of complete metric space. Consequently, the obtained results encompass various generalizations of the Banach contraction principle. Moreover, some examples and an application to nonlinear fractional differential equation are given to illustrate the usability of the new theory. 展开更多
关键词 fixed points nonlinear fractional differential equations periodic points
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Existence of Positive Solutions of Three-point Boundary Value Problem for Higher Order Nonlinear Fractional Differential Equations 被引量:2
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作者 韩仁基 葛建生 蒋威 《Chinese Quarterly Journal of Mathematics》 CSCD 2012年第4期516-525,共10页
In this paper, we consider the positive solutions of fractional three-point boundary value problem of the form Dο^α+u(t)+f(t,u(t),u'(t),…,u^(n-3)(5),u^(n-2)(t))=0,u^(i)(0)=0,0≤i≤n-2,u^(n-... In this paper, we consider the positive solutions of fractional three-point boundary value problem of the form Dο^α+u(t)+f(t,u(t),u'(t),…,u^(n-3)(5),u^(n-2)(t))=0,u^(i)(0)=0,0≤i≤n-2,u^(n-2)(1)-βu^(n-2)(ξ)=0,where 0〈t〈1,n-1〈α≤n,n≥2,ξ Е(0,1),βξ^a-n〈1. We first transform it into another equivalent boundary value problem. Then, we derive the Green's function for the equivalent boundary value problem and show that it satisfies certain properties. At last, by using some fixed-point theorems, we obtain the existence of positive solution for this problem. Example is given to illustrate the effectiveness of our result. 展开更多
关键词 nonlinear fractional differential equation three-point boundary value problem positive solutions green’s function banach contraction mapping fixed point theorem in cones
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Finite-Time Stability for Nonlinear Fractional Differential Equations with Time Delay 被引量:1
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作者 HE Huazhen KOU Chunhai 《Journal of Donghua University(English Edition)》 CAS 2022年第5期446-453,共8页
The finite-time stability and the finite-time contractive stability of solutions for nonlinear fractional differential equations with bounded delay are investigated. The derivative of Lyapunov function along solutions... The finite-time stability and the finite-time contractive stability of solutions for nonlinear fractional differential equations with bounded delay are investigated. The derivative of Lyapunov function along solutions of the considered system is defined in terms of the Caputo fractional Dini derivative. Based on the Lyapunov-Razumikhin method, several sufficient criteria are established to guarantee the finite-time stability and the finite-time contractive stability of solutions for the related systems. An example is provided to illustrate the effectiveness of the obtained results. 展开更多
关键词 finite-time stability nonlinear fractional differential equation time delay Caputo fractional Dini derivative Lyapunov-Razumikhin method
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The Solution to Impulse Boundary Value Problem for a Class of Nonlinear Fractional Functional Differential Equations
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作者 HAN Ren-ji ZHO U Xian-feng +1 位作者 LI Xiang JIANG Wei 《Chinese Quarterly Journal of Mathematics》 CSCD 2014年第3期400-411,共12页
In this paper, we investigate the existence of solution for a class of impulse boundary value problem of nonlinear fractional functional differential equation of mixed type. We obtain the existence results of solution... In this paper, we investigate the existence of solution for a class of impulse boundary value problem of nonlinear fractional functional differential equation of mixed type. We obtain the existence results of solution by applying some well-known fixed point theorems. An example is given to illustrate the effectiveness of our result. 展开更多
关键词 nonlinear fractional functional differential equation mixed type impulse boundary value problem fixed point theorem
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ADI Finite Element Method for 2D Nonlinear Time Fractional Reaction-Subdiffusion Equation
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作者 Peng Zhu Shenglan Xie 《American Journal of Computational Mathematics》 2016年第4期336-356,共21页
In this paper, an alternating direction Galerkin finite element method is presented for solving 2D time fractional reaction sub-diffusion equation with nonlinear source term. Firstly, one order implicit-explicit metho... In this paper, an alternating direction Galerkin finite element method is presented for solving 2D time fractional reaction sub-diffusion equation with nonlinear source term. Firstly, one order implicit-explicit method is used for time discretization, then Galerkin finite element method is adopted for spatial discretization and obtain a fully discrete linear system. Secondly, Galerkin alternating direction procedure for the system is derived by adding an extra term. Finally, the stability and convergence of the method are analyzed rigorously. Numerical results confirm the accuracy and efficiency of the proposed method. 展开更多
关键词 nonlinear fractional differential Equation Alternating Direction Implicit Method Finite Element Method Riemann-Liouville fractional Derivative
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linear and nonlinear fractional differential equation modified Riemann–Liouville derivatives exact solutions fractional auxiliary sub-equation expansion method Mittag–Leffler function method 被引量:4
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作者 Emad A-B.Abdel-Salam Gamal F.Hassan 《Communications in Theoretical Physics》 SCIE CAS CSCD 2016年第2期127-135,共9页
In this paper, the fractional auxiliary sub-equation expansion method is proposed to solve nonlinear fractional differential equations. To illustrate the effectiveness of the method, we discuss the space-time fraction... In this paper, the fractional auxiliary sub-equation expansion method is proposed to solve nonlinear fractional differential equations. To illustrate the effectiveness of the method, we discuss the space-time fractional Kd V equation, the space-time fractional RLW equation, the space-time fractional Boussinesq equation, and the(3+1)-spacetime fractional ZK equation. The solutions are expressed in terms of fractional hyperbolic and fractional trigonometric functions. These solutions are useful to understand the mechanisms of the complicated nonlinear physical phenomena and fractional differential equations. Among these solutions, some are found for the first time. The analytical solution of homogenous linear FDEs with constant coefficients are obtained by using the series and the Mittag–Leffler function methods. The obtained results recover the well-know solutions when α = 1. 展开更多
关键词 Solutions to Class of Linear and nonlinear fractional differential Equations
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Solving Nonlinear Fractional Differential Equation by Generalized Mittag-Leffler Function Method 被引量:1
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作者 A.A.M.Arafa Z.Rida +1 位作者 A.A.Mohammadein H.M.Ali 《Communications in Theoretical Physics》 SCIE CAS CSCD 2013年第6期661-663,共3页
In this paper, we use Mittag-Leffler function method for solving some nonlinear fractional differential equations. A new solution is constructed in power series. The fractional derivatives are described by Caputo'... In this paper, we use Mittag-Leffler function method for solving some nonlinear fractional differential equations. A new solution is constructed in power series. The fractional derivatives are described by Caputo's sense. To illustrate the reliability of the method, some examples are provided. 展开更多
关键词 nonlinear fractional differential equations Mittag-Leffler function Caputo fractional derivative
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LOCAL GAUSSIAN-COLLOCATION SCHEME TO APPROXIMATE THE SOLUTION OF NONLINEAR FRACTIONAL DIFFERENTIAL EQUATIONS USING VOLTERRA INTEGRAL EQUATIONS
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作者 Pouria Assari Fatemeh Asadi-Mehregan Mehdi Dehghan 《Journal of Computational Mathematics》 SCIE CSCD 2021年第2期261-282,共22页
This work describes an accurate and effective method for numerically solving a class of nonlinear fractional differential equations.To start the method,we equivalently convert these types of differential equations to ... This work describes an accurate and effective method for numerically solving a class of nonlinear fractional differential equations.To start the method,we equivalently convert these types of differential equations to nonlinear fractional Volterra integral equations of the second kind by integrating from both sides of them.Afterward,the solution of the mentioned Volterra integral equations can be estimated using the collocation method based on locally supported Gaussian functions.The local Gaussian-collocation scheme estimates the unknown function utilizing a small set of data instead of all points in the solution domain,so the proposed method uses much less computer memory and volume computing in comparison with global cases.We apply the composite non-uniform Gauss-Legendre quadrature formula to estimate singular-fractional integrals in the method.Because of the fact that the proposed scheme requires no cell structures on the domain,it is a meshless method.Furthermore,we obtain the error analysis of the proposed method and demon-strate that the convergence rate of the approach is arbitrarily high.Illustrative examples clearly show the reliability and efficiency of the new technique and confirm the theoretical error estimates. 展开更多
关键词 nonlinear fractional differential equation Volterra integral equation Gaussian-collocation method Meshless method Error analysis
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consistent Riccati expansion fractional partial differential equation Riccati equation modified Riemann–Liouville fractional derivative exact solution 被引量:7
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作者 黄晴 王丽真 左苏丽 《Communications in Theoretical Physics》 SCIE CAS CSCD 2016年第2期177-184,共8页
In this paper, a consistent Riccati expansion method is developed to solve nonlinear fractional partial differential equations involving Jumarie's modified Riemann–Liouville derivative. The efficiency and power of t... In this paper, a consistent Riccati expansion method is developed to solve nonlinear fractional partial differential equations involving Jumarie's modified Riemann–Liouville derivative. The efficiency and power of this approach are demonstrated by applying it successfully to some important fractional differential equations, namely, the time fractional Burgers, fractional Sawada–Kotera, and fractional coupled mKdV equation. A variety of new exact solutions to these equations under study are constructed. 展开更多
关键词 Consistent Riccati Expansion Method and Its Applications to nonlinear fractional Partial differential Equations
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POSITIVE SOLUTIONS TO BOUNDARY VALUE PROBLEMS OF FRACTIONAL DIFFERENTIAL EQUATIONS WITH PARAMETER
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作者 Qi Wang Dicheng Lu +1 位作者 Rui Wang Yayun Fang 《Annals of Differential Equations》 2014年第2期191-198,共8页
In this paper, we consider a class of nonlinear fractional differential equation boun- dary value problem with a parameter. By some fixed point theorems, sufficient con- ditions for the existence, nonexistence and mul... In this paper, we consider a class of nonlinear fractional differential equation boun- dary value problem with a parameter. By some fixed point theorems, sufficient con- ditions for the existence, nonexistence and multiplicity of positive solutions to the system are obtained. An example is given to illustrate the main results. 展开更多
关键词 nonlinear fractional differential equation boundary value problem positive solution fixed point theorem
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New Exact Solutions of Time Fractional Gardner Equation by Using New Version of F-Expansion Method 被引量:10
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作者 Yusuf Pandir Hasan Huseyin Duzgun 《Communications in Theoretical Physics》 SCIE CAS CSCD 2017年第1期9-14,共6页
In this article, we consider analytical solutions of the time fractional derivative Gardner equation by using the new version of F-expansion method. With this proposed method multiple Jacobi elliptic functions are sit... In this article, we consider analytical solutions of the time fractional derivative Gardner equation by using the new version of F-expansion method. With this proposed method multiple Jacobi elliptic functions are situated in the solution function. As a result, various exact analytical solutions consisting of single and combined Jacobi elliptic functions solutions are obtained. 展开更多
关键词 new version of F-expansion method nonlinear differential equations with fractional derivatives single and combined Jacobi elliptic functions solutions
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