Existence and uniqueness for a coupled system of fractional equations involving Riemann-Liouville and Caputo derivatives with coupled Riemann-Stieltjes integro-multipoint boundary conditions

Ymnah Alruwaily; Lamya Almaghamsi; Kulandhaivel Karthikeyan; El-sayed El-hady; Ymnah Alruwaily; Lamya Almaghamsi; Kulandhaivel Karthikeyan; El-sayed El-hady

doi:10.3934/math.2023510

AIMS Mathematics

2023, Volume 8, Issue 5: 10067-10094. doi: 10.3934/math.2023510

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Existence and uniqueness for a coupled system of fractional equations involving Riemann-Liouville and Caputo derivatives with coupled Riemann-Stieltjes integro-multipoint boundary conditions

1.
Mathematics Department, College of Science, Jouf University, Sakaka P.O.Box 2014, Saudi Arabia
2.
Department of Mathematics, College of Science, University of Jeddah, P.O.Box 80327 Jeddah 21589, Saudi Arabia
3.
Department of Mathematics, KPR Institute of Engineering and Technology, Coimbatore-641 407, Tamil Nadu, India
4.
Basic Science Department, Faculty of Computers and Informatics, Suez Canal University, Ismailia 41522, Egypt

Received: 20 December 2022 Revised: 09 February 2023 Accepted: 12 February 2023 Published: 24 February 2023
MSC : 26A33, 34A08, 34A12, 47H10

Recently, coupled systems of fractional differential equations play a central role in the modelling of many systems in e.g., financial economics, ecology, and many more. This study investigates the existence and uniqueness of solutions for a nonlinear coupled system of fractional differential equations involving Riemann-Liouville and Caputo derivatives with coupled Riemann-Stieltjes integro-multipoint boundary conditions. The main tools are known fixed point theorems, namely, Leray-Schauder alternative, Banach fixed point theorem, and the Krasnoselskii fixed point theorem. The new system, which can be considered as a generalized version of many previous fascinating systems, is where the article's novelty lies. Examples are presented to illustrate the results. In this way, we generalize several earlier results.
- coupled system of fractional differential equations,
- integro-multipoint boundary conditions,
- fixed point theorems
Citation: Ymnah Alruwaily, Lamya Almaghamsi, Kulandhaivel Karthikeyan, El-sayed El-hady. Existence and uniqueness for a coupled system of fractional equations involving Riemann-Liouville and Caputo derivatives with coupled Riemann-Stieltjes integro-multipoint boundary conditions[J]. AIMS Mathematics, 2023, 8(5): 10067-10094. doi: 10.3934/math.2023510

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Abstract

Recently, coupled systems of fractional differential equations play a central role in the modelling of many systems in e.g., financial economics, ecology, and many more. This study investigates the existence and uniqueness of solutions for a nonlinear coupled system of fractional differential equations involving Riemann-Liouville and Caputo derivatives with coupled Riemann-Stieltjes integro-multipoint boundary conditions. The main tools are known fixed point theorems, namely, Leray-Schauder alternative, Banach fixed point theorem, and the Krasnoselskii fixed point theorem. The new system, which can be considered as a generalized version of many previous fascinating systems, is where the article's novelty lies. Examples are presented to illustrate the results. In this way, we generalize several earlier results.

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