Analysis of nonlinear coupled Caputo fractional differential equations with boundary conditions in terms of sum and difference of the governing functions

Ahmed Alsaedi; Fawziah M. Alotaibi; Bashir Ahmad; Ahmed Alsaedi; Fawziah M. Alotaibi; Bashir Ahmad

doi:10.3934/math.2022463

AIMS Mathematics

2022, Volume 7, Issue 5: 8314-8329. doi: 10.3934/math.2022463

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Analysis of nonlinear coupled Caputo fractional differential equations with boundary conditions in terms of sum and difference of the governing functions

Nonlinear Analysis and Applied Mathematics (NAAM)-Research Group, Department of Mathematics, Faculty of Science, King Abdulaziz University, P.O. Box 80203, Jeddah 21589, Saudi Arabia

Received: 29 December 2021 Revised: 04 February 2022 Accepted: 17 February 2022 Published: 28 February 2022
MSC : 34A08, 34B15

In this paper, we introduce a new class of nonlocal multipoint-integral boundary conditions with respect to the sum and difference of the governing functions and analyze a coupled system of nonlinear Caputo fractional differential equations equipped with these conditions. The existence and uniqueness results for the given problem are proved via the tools of the fixed point theory. We also discuss the case of nonlinear Riemann-Liouville integral boundary conditions. The obtained results are well-illustrated with examples.
- fractional differential system,
- multipoint-integral boundary conditions,
- existence,
- fixed point
Citation: Ahmed Alsaedi, Fawziah M. Alotaibi, Bashir Ahmad. Analysis of nonlinear coupled Caputo fractional differential equations with boundary conditions in terms of sum and difference of the governing functions[J]. AIMS Mathematics, 2022, 7(5): 8314-8329. doi: 10.3934/math.2022463

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Abstract

In this paper, we introduce a new class of nonlocal multipoint-integral boundary conditions with respect to the sum and difference of the governing functions and analyze a coupled system of nonlinear Caputo fractional differential equations equipped with these conditions. The existence and uniqueness results for the given problem are proved via the tools of the fixed point theory. We also discuss the case of nonlinear Riemann-Liouville integral boundary conditions. The obtained results are well-illustrated with examples.

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