Application of a tripled fixed point theorem to investigate a nonlinear system of fractional order hybrid sequential integro-differential equations

Muhammed Jamil; Rahmat Ali Khan; Kamal Shah; Bahaaeldin Abdalla; Thabet Abdeljawad; Muhammed Jamil; Rahmat Ali Khan; Kamal Shah; Bahaaeldin Abdalla; Thabet Abdeljawad

doi:10.3934/math.20221029

AIMS Mathematics

2022, Volume 7, Issue 10: 18708-18728. doi: 10.3934/math.20221029

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Application of a tripled fixed point theorem to investigate a nonlinear system of fractional order hybrid sequential integro-differential equations

1.
Department of Mathematics, University of Malakand, Chakdara Dir (Lower), Khyber Pakhtunkhawa, Pakistan
2.
Department of Mathematics and Sciences, Prince Sultan University, P.O. Box 66833, Riyadh 11586, Saudi Arabia
3.
Department of Medical Research, China Medical University, Taichung 40402, Taiwan

Received: 13 July 2022 Revised: 08 August 2022 Accepted: 18 August 2022 Published: 23 August 2022
MSC : 34A08, 47H08, 34A38

The goal of this manuscript is to study the existence theory of solution for a nonlinear boundary value problem of tripled system of fractional order hybrid sequential integro-differential equations. The analysis depends on some results from fractional calculus and fixed point theory. As a result, we generalized Darbo's fixed point theorem to form an updated version of tripled fixed point theorem to investigate the proposed system. Also, Hyres-Ulam and generalized Hyres-Ulam stabilities results are established for the considered system. For the illustration of our main results, we provide an example.
- measure of non-compactness,
- tripled system,
- Darbo's fixed point theorem,
- Hyers-Ulam stability
Citation: Muhammed Jamil, Rahmat Ali Khan, Kamal Shah, Bahaaeldin Abdalla, Thabet Abdeljawad. Application of a tripled fixed point theorem to investigate a nonlinear system of fractional order hybrid sequential integro-differential equations[J]. AIMS Mathematics, 2022, 7(10): 18708-18728. doi: 10.3934/math.20221029

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Abstract

The goal of this manuscript is to study the existence theory of solution for a nonlinear boundary value problem of tripled system of fractional order hybrid sequential integro-differential equations. The analysis depends on some results from fractional calculus and fixed point theory. As a result, we generalized Darbo's fixed point theorem to form an updated version of tripled fixed point theorem to investigate the proposed system. Also, Hyres-Ulam and generalized Hyres-Ulam stabilities results are established for the considered system. For the illustration of our main results, we provide an example.

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