Title: On a coupled nonlinear fractional integro-differential equations with coupled non-local generalised fractional integral boundary conditions

Authors: Subramanian Muthaiah

Addresses: Department of Mathematics, KPR Institute of Engineering and Technology, Coimbatore, Tamilnadu, 641407, India

Abstract: We investigate a coupled Liouville-Caputo fractional integro-differential equations (CLCFIDEs) with nonlinearities that depend on the lower order fractional derivatives of the unknown functions, and also fractional integrals of the unknown functions supplemented with the coupled non-local generalised Riemann-Liouville fractional integral (GRLFI) boundary conditions. The existence and uniqueness results have endorsed by Leray-Schauder nonlinear alternative, and Banach fixed point theorem respectively. Sufficient examples have also been supplemented to substantiate the proof, and we have discussed some variants of the given problem.

Keywords: fractional differential equations; Liouville-Caputo derivatives; coupled system; generalised fractional integrals; non-local; existence; fixed point.

DOI: 10.1504/IJDSDE.2022.123392

International Journal of Dynamical Systems and Differential Equations, 2022 Vol.12 No.2, pp.121 - 145

Received: 07 May 2019
Accepted: 28 Sep 2019
Published online: 20 Jun 2022 *

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