Existence results for a coupled system of nonlinear multi‐term fractional differential equations with anti‐periodic type coupled nonlocal boundary conditions

This paper is a survey of the recent results of the author for various classes of boundary value problems for Hilfer fractional differential equations and inclusions of fractional order in (1,2] supplemented with different kinds of nonlocal boundary conditions.

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Solving a linear fractional equation with nonlocal boundary conditions based on multiscale orthonormal bases method in the reproducing kernel space

International Journal of Nonlinear Sciences and Numerical Simulation ◽

10.1515/ijnsns-2019-0291 ◽

2020 ◽

Vol 0 (0) ◽

Author(s):

Wei Jiang ◽

Zhong Chen ◽

Ning Hu ◽

Yali Chen

Keyword(s):

Differential Equations ◽

Boundary Conditions ◽

Fractional Differential Equations ◽

Reproducing Kernel ◽

Nonlocal Boundary ◽

Nonlocal Boundary Conditions ◽

Kernel Space ◽

Reproducing Kernel Space ◽

Orthonormal Bases ◽

Fractional Differential

AbstractIn recent years, the study of fractional differential equations has become a hot spot. It is more difficult to solve fractional differential equations with nonlocal boundary conditions. In this article, we propose a multiscale orthonormal bases collocation method for linear fractional-order nonlocal boundary value problems. In algorithm construction, the solution is expanded by the multiscale orthonormal bases of a reproducing kernel space. The nonlocal boundary conditions are transformed into operator equations, which are involved in finding the collocation coefficients as constrain conditions. In theory, the convergent order and stability analysis of the proposed method are presented rigorously. Finally, numerical examples show the stability, accuracy and effectiveness of the method.

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Existence of solutions for a system of fractional differential equations with coupled nonlocal boundary conditions

Fractional Calculus and Applied Analysis ◽

10.1515/fca-2018-0024 ◽

2018 ◽

Vol 21 (2) ◽

pp. 423-441 ◽

Cited By ~ 28

Author(s):

Bashir Ahmad ◽

Rodica Luca

Keyword(s):

Differential Equations ◽

Boundary Conditions ◽

Fractional Differential Equations ◽

Existence Of Solutions ◽

Nonlocal Boundary ◽

Nonlocal Boundary Conditions ◽

Fractional Integrals ◽

Nonlinear Alternative ◽

Coupled Boundary Conditions ◽

Fractional Differential

AbstractWe study the existence of solutions for a system of nonlinear Caputo fractional differential equations with coupled boundary conditions involving Riemann-Liouville fractional integrals, by using the Schauder fixed point theorem and the nonlinear alternative of Leray-Schauder type. Two examples are given to support our main results.

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Existence and Uniqueness Results for a Coupled System of Caputo-Hadamard Fractional Differential Equations with Nonlocal Hadamard Type Integral Boundary Conditions

Fractal and Fractional ◽

10.3390/fractalfract4020013 ◽

2020 ◽

Vol 4 (2) ◽

pp. 13 ◽

Cited By ~ 1

Author(s):

Shorog Aljoudi ◽

Bashir Ahmad ◽

Ahmed Alsaedi

Keyword(s):

Differential Equations ◽

Boundary Conditions ◽

Fractional Differential Equations ◽

Existence And Uniqueness ◽

Nonlocal Boundary ◽

Integral Boundary Conditions ◽

Coupled System ◽

Integral Boundary ◽

Uniqueness Results ◽

Fractional Differential

In this paper, we study a coupled system of Caputo-Hadamard type sequential fractional differential equations supplemented with nonlocal boundary conditions involving Hadamard fractional integrals. The sufficient criteria ensuring the existence and uniqueness of solutions for the given problem are obtained. We make use of the Leray-Schauder alternative and contraction mapping principle to derive the desired results. Illustrative examples for the main results are also presented.

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