Mönch's fixed point theorem in investigating the existence of a solution to a system of sequential fractional differential equations

Abeer Al Elaiw; Murugesan Manigandan; Muath Awadalla; Kinda Abuasbeh; Abeer Al Elaiw; Murugesan Manigandan; Muath Awadalla; Kinda Abuasbeh

doi:10.3934/math.2023134

AIMS Mathematics

2023, Volume 8, Issue 2: 2591-2610. doi: 10.3934/math.2023134

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Research article

Mönch's fixed point theorem in investigating the existence of a solution to a system of sequential fractional differential equations

1.
Department of Mathematics and Statistics, College of Science, King Faisal University, Hafuf, Al Ahsa 31982, Saudi Arabia
2.
Sri Ramakrishna Mission Vidyalaya College of Arts and Science, Tamil Nadu, Coimbatore 641020, India

Received: 19 September 2022 Revised: 18 October 2022 Accepted: 25 October 2022 Published: 08 November 2022
MSC : 26A33, 34B15, 34B18

In this article, the existence of a solution to a system of fractional equations of sequential type was investigated via Mönch's fixed point theorem. In addition, the stability of this solutions was verified by the Ulam-Hyers method. Finally, an applied example is presented to illustrate the theoretical results obtained from the existence results.
- Caputo derivatives,
- Mönch's fixed point,
- sequential fractional derivative,
- existence,
- stability
Citation: Abeer Al Elaiw, Murugesan Manigandan, Muath Awadalla, Kinda Abuasbeh. Mönch's fixed point theorem in investigating the existence of a solution to a system of sequential fractional differential equations[J]. AIMS Mathematics, 2023, 8(2): 2591-2610. doi: 10.3934/math.2023134

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Abstract

In this article, the existence of a solution to a system of fractional equations of sequential type was investigated via Mönch's fixed point theorem. In addition, the stability of this solutions was verified by the Ulam-Hyers method. Finally, an applied example is presented to illustrate the theoretical results obtained from the existence results.

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