scholarly journals Sequential fractional pantograph differential equations with nonlocal boundary conditions: Uniqueness and Ulam-Hyers-Rassias stability

2022 ◽  
Author(s):  
Houas MOHAMED
Keyword(s):  
Differential Equations ◽  
Boundary Conditions ◽  
Nonlocal Boundary ◽  
Nonlocal Boundary Conditions ◽  
Rassias Stability

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

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.

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

2018 ◽  
Vol 21 (2) ◽  
pp. 423-441 ◽  
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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