Existence of Solutions for Coupled Higher-Order Fractional Integro-Differential Equations with Nonlocal Integral and Multi-Point Boundary Conditions Depending on Lower-Order Fractional Derivatives and Integrals

Muthaiah Subramanian, Jehad Alzabut, Mohamed I. Abbas, Chatthai Thaiprayoon and Weerawat Sudsutad
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Muthaiah Subramanian: Department of Mathematics, KPR Institute of Engineering and Technology, Coimbatore 641407, India
Jehad Alzabut: Deparment of Mathematics and Sciences, Prince Sultan University, Riyadh 11586, Saudi Arabia
Mohamed I. Abbas: Department of Mathematics and Computer Science, Faculty of Science, Alexandria University, Alexandria 21511, Egypt
Chatthai Thaiprayoon: Research Group of Theoretical and Computation in Applied Science, Department of Mathematics, Faculty of Science, Burapha University, Chonburi 20131, Thailand
Weerawat Sudsutad: Department of Statistics, Faculty of Science, Ramkhamhaeng University, Bangkok 10240, Thailand

Mathematics, 2022, vol. 10, issue 11, 1-19

Abstract: In this article, we investigate the existence and uniqueness of solutions for a nonlinear coupled system of Liouville–Caputo type fractional integro-differential equations supplemented with non-local discrete and integral boundary conditions. The nonlinearity relies both on the unknown functions and their fractional derivatives and integrals in the lower order. The consequence of existence is obtained utilizing the alternative of Leray–Schauder, while the result of uniqueness is based on the concept of Banach contraction mapping. We introduced the concept of unification in the present work with varying parameters of the multi-point and classical integral boundary conditions. With the help of examples, the main results are well demonstrated.

Keywords: coupled system; integro-differential equations; Caputo derivatives; multi-point; integral boundary conditions; fixed point theorems (search for similar items in EconPapers)
JEL-codes: C (search for similar items in EconPapers)
Date: 2022
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