New results for a coupled system of ABR fractional differential equations with sub-strip boundary conditions

Mohammed A. Almalahi; Satish K. Panchal; Tariq A. Aljaaidi; Fahd Jarad; Mohammed A. Almalahi; Satish K. Panchal; Tariq A. Aljaaidi; Fahd Jarad

doi:10.3934/math.2022244

AIMS Mathematics

2022, Volume 7, Issue 3: 4386-4404. doi: 10.3934/math.2022244

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Research article

New results for a coupled system of ABR fractional differential equations with sub-strip boundary conditions

1.
Department of Mathematics, Hajjah University, Hajjah, Yemen
2.
Department of Mathematics, Dr. Babasaheb Ambedkar Marathwada University, Aurangabad (M.S), 431001, India
3.
Department of Mathematics, Çankaya University, Etimesgut, Ankara, 06790, Turkey
4.
Department of Medical Research, China Medical University Hospital, China Medical University, Taichung, Taiwan

Received: 09 October 2021 Revised: 05 December 2021 Accepted: 13 December 2021 Published: 21 December 2021
MSC : 34A08, 34B15, 34A12, 47H10

In this article, we investigate sufficient conditions for the existence, uniqueness and Ulam-Hyers (UH) stability of solutions to a new system of nonlinear ABR fractional derivative of order $ 1 < \varrho\leq 2 $ subjected to multi-point sub-strip boundary conditions. We discuss the existence and uniqueness of solutions with the assistance of Leray-Schauder alternative theorem and Banach's contraction principle. In addition, by using some mathematical techniques, we examine the stability results of Ulam-Hyers (UH). Finally, we provide one example in order to show the validity of our results.
- sub-strip boundary conditions,
- coupled system,
- existence,
- fixed point theorem
Citation: Mohammed A. Almalahi, Satish K. Panchal, Tariq A. Aljaaidi, Fahd Jarad. New results for a coupled system of ABR fractional differential equations with sub-strip boundary conditions[J]. AIMS Mathematics, 2022, 7(3): 4386-4404. doi: 10.3934/math.2022244

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Abstract

In this article, we investigate sufficient conditions for the existence, uniqueness and Ulam-Hyers (UH) stability of solutions to a new system of nonlinear ABR fractional derivative of order $ 1 < \varrho\leq 2 $ subjected to multi-point sub-strip boundary conditions. We discuss the existence and uniqueness of solutions with the assistance of Leray-Schauder alternative theorem and Banach's contraction principle. In addition, by using some mathematical techniques, we examine the stability results of Ulam-Hyers (UH). Finally, we provide one example in order to show the validity of our results.

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