Solvability and stability analysis of a coupled system involving generalized fractional derivatives

Abdallah Djaout; Maamar Benbachir; Mustapha Lakrib; Mohammed M. Matar; Aziz Khan; Thabet Abdeljawad; Abdallah Djaout; Maamar Benbachir; Mustapha Lakrib; Mohammed M. Matar; Aziz Khan; Thabet Abdeljawad

doi:10.3934/math.2023393

AIMS Mathematics

2023, Volume 8, Issue 4: 7817-7839. doi: 10.3934/math.2023393

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Solvability and stability analysis of a coupled system involving generalized fractional derivatives

1.
Faculty of Sciences, Saad Dahlab University, Blida, Algeria
2.
National Higher School of Mathematics, Algiers, Algeria
3.
Laboratory of Mathematics, Djillali Liabès University, Sidi Bel Abbès, Algeria
4.
Department of Mathematics, Al-Azhar University-Gaza, Palestine
5.
Department of Mathematics and Sciences, Prince Sultan University, P.O. Box 66833, Riyadh 11586, Saudi Arabia
6.
Department of Medical Research, China Medical University, Taichung 40402, Taiwan
7.
Department of Mathematics, Kyung Hee University, 26 Kyungheedae-ro, Dongdaemun-gu, Seoul 02447, Korea

Received: 23 October 2022 Revised: 05 January 2023 Accepted: 09 January 2023 Published: 31 January 2023
MSC : 26A33, 34B18, 34B27

In this article, we investigate the existence of unique maximal and minimal solutions for a coupled differential system in terms of generalized fractional derivative with arbitrary order. The iterative technique of a fixed point operator together with the properties of green's function are used basically. Moreover, we investigate the generalized Ulam-Hyers stability of the solution for the given coupled system. Finally, some examples are given to illustrate the theoretic results.
- existence and uniqueness,
- generalized fractional derivative and integral,
- boundary value problem,
- minimal and maximal solutions,
- Ulam-Hyers
Citation: Abdallah Djaout, Maamar Benbachir, Mustapha Lakrib, Mohammed M. Matar, Aziz Khan, Thabet Abdeljawad. Solvability and stability analysis of a coupled system involving generalized fractional derivatives[J]. AIMS Mathematics, 2023, 8(4): 7817-7839. doi: 10.3934/math.2023393

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Abstract

In this article, we investigate the existence of unique maximal and minimal solutions for a coupled differential system in terms of generalized fractional derivative with arbitrary order. The iterative technique of a fixed point operator together with the properties of green's function are used basically. Moreover, we investigate the generalized Ulam-Hyers stability of the solution for the given coupled system. Finally, some examples are given to illustrate the theoretic results.

References

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