Existence of Solutions for Coupled System of Sequential Liouville–Caputo-Type Fractional Integrodifferential Equations

The present investigation aims to establish the existence and uniqueness of solutions for a system containing sequential fractional differential equations. Furthermore, boundary conditions that include the Riemann–Liouville fractional integral are taken into consideration. The existence of unknown f...

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Bibliographic Details
Published in:Fractal and fractional Vol. 7; no. 11; p. 800
Main Authors: Murugesan, Manigandan, Muthaiah, Subramanian, Vadivel, Rajarathinam, Unyong, Bundit
Format: Journal Article
Language:English
Published: Basel MDPI AG 01.11.2023
Subjects:
Boundary conditions
Boundary value problems
Differential equations
existence
Fixed points (mathematics)
Fractional calculus
fractional integrodifferential equations
Integrals
Iterative methods
Liouville–Caputo derivatives
Mathematical analysis
Mathematical functions
Riemann–Liouville integrals
sequential derivatives
uniqueness
ISSN:2504-3110, 2504-3110
Online Access:Get full text
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Summary:The present investigation aims to establish the existence and uniqueness of solutions for a system containing sequential fractional differential equations. Furthermore, boundary conditions that include the Riemann–Liouville fractional integral are taken into consideration. The existence of unknown functions, fractional derivatives, and fractional integrals at lower orders are necessary for the nonlinearity to exist. In order to provide proofs for the results presented in this study, the Leray–Schauder alternative and the Banach fixed-point theorem are utilised. Finally, examples are used to support the main results.
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ISSN:2504-3110
2504-3110
DOI:10.3390/fractalfract7110800