Existence results for coupled differential equations of non-integer order with Riemann-Liouville, Erdélyi-Kober integral conditions

Dumitru Baleanu; S. Hemalatha; P. Duraisamy; P. Pandiyan; Subramanian Muthaiah; Dumitru Baleanu; S. Hemalatha; P. Duraisamy; P. Pandiyan; Subramanian Muthaiah

doi:10.3934/math.2021752

AIMS Mathematics

2021, Volume 6, Issue 12: 13004-13023. doi: 10.3934/math.2021752

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Research article

Existence results for coupled differential equations of non-integer order with Riemann-Liouville, Erdélyi-Kober integral conditions

1.
Department of Mathematics, Cankaya University, Ankara, Turkey
2.
Institute of Space Science, Magurele-Bucharest, Romania
3.
Department of Medical Research, China Medical University, Taichung, Taiwan
4.
Department of Mathematics, Sasurie College of Arts and Science, Vijayamangalam, India
5.
Department of Mathematics, Gobi Arts and Science College, Gobichettipalayam, India
6.
Department of Electrical and electronics engineering, KPR Institute of Engineering and Technology, Coimbatore, India
7.
Department of Mathematics, KPR Institute of Engineering and Technology, Coimbatore, India

Received: 13 February 2021 Accepted: 26 August 2021 Published: 14 September 2021
MSC : 26A33, 34A08, 34B15

This paper proposes the existence and uniqueness of a solution for a coupled system that has fractional differential equations through Erdélyi-Kober and Riemann-Liouville fractional integral boundary conditions. The existence of the solution for the coupled system by adopting the Leray-Schauder alternative. The uniqueness of solution for the problem can be found using Banach fixed point theorem. In order to verify the proposed criterion, some numerical examples are also discussed.
- Caputo derivatives,
- Erdélyi-Kober integrals,
- Riemann-Liouville integrals,
- coupled system,
- existence,
- fixed point
Citation: Dumitru Baleanu, S. Hemalatha, P. Duraisamy, P. Pandiyan, Subramanian Muthaiah. Existence results for coupled differential equations of non-integer order with Riemann-Liouville, Erdélyi-Kober integral conditions[J]. AIMS Mathematics, 2021, 6(12): 13004-13023. doi: 10.3934/math.2021752

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Abstract

This paper proposes the existence and uniqueness of a solution for a coupled system that has fractional differential equations through Erdélyi-Kober and Riemann-Liouville fractional integral boundary conditions. The existence of the solution for the coupled system by adopting the Leray-Schauder alternative. The uniqueness of solution for the problem can be found using Banach fixed point theorem. In order to verify the proposed criterion, some numerical examples are also discussed.

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