A study of coupled nonlinear generalized fractional differential equations with coupled nonlocal multipoint Riemann-Stieltjes and generalized fractional integral boundary conditions

Bashir Ahmad; Ahmed Alsaedi; Areej S. Aljahdali; Sotiris K. Ntouyas; Bashir Ahmad; Ahmed Alsaedi; Areej S. Aljahdali; Sotiris K. Ntouyas

doi:10.3934/math.2024078

AIMS Mathematics

2024, Volume 9, Issue 1: 1576-1594. doi: 10.3934/math.2024078

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A study of coupled nonlinear generalized fractional differential equations with coupled nonlocal multipoint Riemann-Stieltjes and generalized fractional integral boundary conditions

1.
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
2.
Department of Mathematics, University of Ioannina, 451 10 Ioannina, Greece

Received: 16 October 2023 Revised: 24 November 2023 Accepted: 04 December 2023 Published: 13 December 2023
MSC : 34A08, 26A33, 34B15

This paper was concerned with the existence and uniqueness results for a coupled system of nonlinear generalized fractional differential equations supplemented with a new class of nonlocal coupled multipoint boundary conditions containing Riemann-Stieltjes and generalized fractional integrals. The nonlinearities in the given system depend on the unknown functions as well as their lower order generalized fractional derivatives. We made use of the Leray-Schauder alternative and Banach contraction mapping principle to obtain the desired results. An illustrative example was also discussed. The paper concluded with some interesting observations.
- generalized fractional integral and derivative operators,
- multipoint,
- integral boundary conditions,
- existence,
- fixed point
Citation: Bashir Ahmad, Ahmed Alsaedi, Areej S. Aljahdali, Sotiris K. Ntouyas. A study of coupled nonlinear generalized fractional differential equations with coupled nonlocal multipoint Riemann-Stieltjes and generalized fractional integral boundary conditions[J]. AIMS Mathematics, 2024, 9(1): 1576-1594. doi: 10.3934/math.2024078

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Abstract

This paper was concerned with the existence and uniqueness results for a coupled system of nonlinear generalized fractional differential equations supplemented with a new class of nonlocal coupled multipoint boundary conditions containing Riemann-Stieltjes and generalized fractional integrals. The nonlinearities in the given system depend on the unknown functions as well as their lower order generalized fractional derivatives. We made use of the Leray-Schauder alternative and Banach contraction mapping principle to obtain the desired results. An illustrative example was also discussed. The paper concluded with some interesting observations.

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