Sufficient conditions for existence of solutions of nonlinear differential equations with nonlocal boundary conditions

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 of solutions for sequential fractional integro-differential equations and inclusions with nonlocal boundary conditions

Applied Mathematics and Computation ◽

10.1016/j.amc.2018.07.025 ◽

2018 ◽

Vol 339 ◽

pp. 516-534 ◽

Cited By ~ 11

Author(s):

Bashir Ahmad ◽

Rodica Luca

Keyword(s):

Differential Equations ◽

Boundary Conditions ◽

Existence Of Solutions ◽

Nonlocal Boundary ◽

Nonlocal Boundary Conditions ◽

Differential Equations And Inclusions

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Existence of Solutions for Nonlinear Impulsive Fractional Differential Equations of Orderα∈(2,3]with Nonlocal Boundary Conditions

Abstract and Applied Analysis ◽

10.1155/2012/717235 ◽

2012 ◽

Vol 2012 ◽

pp. 1-26 ◽

Cited By ~ 2

Author(s):

Lihong Zhang ◽

Guotao Wang ◽

Guangxing Song

Keyword(s):

Differential Equations ◽

Fractional Differential Equations ◽

Fixed Point Theorems ◽

Existence Of Solutions ◽

Nonlocal Boundary ◽

Sufficient Conditions ◽

Nonlocal Boundary Conditions ◽

Uniqueness Of Solutions ◽

Impulsive Fractional Differential Equations ◽

Fractional Differential

We investigate the existence and uniqueness of solutions to the nonlocal boundary value problem for nonlinear impulsive fractional differential equations of orderα∈(2,3]. By using some well-known fixed point theorems, sufficient conditions for the existence of solutions are established. Some examples are presented to illustrate the main results.

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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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