Existence and U-H Stability Results for Nonlinear Coupled Fractional Differential Equations with Boundary Conditions Involving Riemann–Liouville and Erdélyi–Kober Integrals

The purpose of this article is to discuss the existence, uniqueness, and Ulam–Hyers stability of solutions to a coupled system of fractional differential equations with Erdélyi–Kober and Riemann–Liouville integral boundary conditions. The Banach fixed point theorem is used to prove the uniqueness of...

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Bibliographic Details
Published in:Fractal and fractional Vol. 6; no. 5; p. 266
Main Authors: Subramanian, Muthaiah, Duraisamy, P., Kamaleshwari, C., Unyong, Bundit, Vadivel, R.
Format: Journal Article
Language:English
Published: Basel MDPI AG 01.05.2022
Subjects:
Boundary conditions
coupled system
Differential equations
Erdélyi–Kober integrals
existence
fixed point
Fixed points (mathematics)
Fractional calculus
Mathematical analysis
Physics
Riemann–Liouville integrals
Stability
Ulam–Hyers stability
Uniqueness
ISSN:2504-3110, 2504-3110
Online Access:Get full text
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Summary:The purpose of this article is to discuss the existence, uniqueness, and Ulam–Hyers stability of solutions to a coupled system of fractional differential equations with Erdélyi–Kober and Riemann–Liouville integral boundary conditions. The Banach fixed point theorem is used to prove the uniqueness of solutions, while the Leray–Schauder alternative is used to prove the existence of solutions. Furthermore, we conclude that the solution to the discussed problem is Hyers–Ulam stable. The results are illustrated with examples.
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ISSN:2504-3110
2504-3110
DOI:10.3390/fractalfract6050266