On the Generalized Liouville–Caputo Type Fractional Differential Equations Supplemented with Katugampola Integral Boundary Conditions

In this study, we examine the existence and Hyers–Ulam stability of a coupled system of generalized Liouville–Caputo fractional order differential equations with integral boundary conditions and a connection to Katugampola integrals. In the first and third theorems, the Leray–Schauder alternative an...

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Bibliographic Details
Published in:Symmetry (Basel) 2022-11, Vol.14 (11), p.2273
Main Authors: Awadalla, Muath, Subramanian, Muthaiah, Abuasbeh, Kinda, Manigandan, Murugesan
Format: Article
Language:English
Subjects:
Banach spaces
Boundary conditions
Boundary value problems
coupled system
Differential equations
existence
Existence theorems
fixed point
Fixed points (mathematics)
Fractional calculus
Functional analysis
generalized fractional derivatives
generalized fractional integrals
Integrals
Mathematical analysis
Parameter modification
Stability analysis
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Summary:In this study, we examine the existence and Hyers–Ulam stability of a coupled system of generalized Liouville–Caputo fractional order differential equations with integral boundary conditions and a connection to Katugampola integrals. In the first and third theorems, the Leray–Schauder alternative and Krasnoselskii’s fixed point theorem are used to demonstrate the existence of a solution. The Banach fixed point theorem’s concept of contraction mapping is used in the second theorem to emphasise the analysis of uniqueness, and the results for Hyers–Ulam stability are established in the next theorem. We establish the stability of Ulam–Hyers using conventional functional analysis. Finally, examples are used to support the results. When a generalized Liouville–Caputo (ρ) parameter is modified, asymmetric results are obtained. This study presents novel results that significantly contribute to the literature on this topic.
ISSN:2073-8994
2073-8994
DOI:10.3390/sym14112273