Utilizing fixed point approach to investigate piecewise equations with non-singular type derivative

Kamal Shah; Thabet Abdeljawad; Bahaaeldin Abdalla; Marwan S Abualrub; Kamal Shah; Thabet Abdeljawad; Bahaaeldin Abdalla; Marwan S Abualrub

doi:10.3934/math.2022804

AIMS Mathematics

2022, Volume 7, Issue 8: 14614-14630. doi: 10.3934/math.2022804

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Utilizing fixed point approach to investigate piecewise equations with non-singular type derivative

1.
Department of Mathematics and Sciences, Prince Sultan University, P.O.Box.11586, Riyadh, Saudi Arabia
2.
Department of Mathematics, University of Malakand, Chakdara Dir(L), P.O.Box. 18000, Khyber Pakhtunkhwa, Pakistan
3.
Department of Medical Research, China Medical University, Taichung 40402, Taiwan
4.
Mathematics Department (Prep. Program), Faculty of Science, Khalifa University, P. O. Box 127788, Abu Dhabi UAE

Received: 10 May 2022 Revised: 31 May 2022 Accepted: 01 June 2022 Published: 08 June 2022
MSC : 26A33, 34A08

In this research work, we establish some new results about piecewise equation involving Caputo Fabrizio derivative (CFD). The concerned class has been recently introduced and these results are fundamental for investigation of qualitative theory and numerical interpretation. We derive some necessary results for the existence, uniqueness and various form of Hyers-Ulam (H-U) type stability for the considered problem. For the required results, we need to utilize usual classical fixed point theorems due to Banach and Krasnoselskii's. Moreover, results devoted to H-U stability are derived by using classical tools of nonlinear functional analysis. Some pertinent test problems are given to demonstrate our results.
- piecewise derivative,
- piecewise integration,
- existence theory,
- stability result
Citation: Kamal Shah, Thabet Abdeljawad, Bahaaeldin Abdalla, Marwan S Abualrub. Utilizing fixed point approach to investigate piecewise equations with non-singular type derivative[J]. AIMS Mathematics, 2022, 7(8): 14614-14630. doi: 10.3934/math.2022804

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Abstract

In this research work, we establish some new results about piecewise equation involving Caputo Fabrizio derivative (CFD). The concerned class has been recently introduced and these results are fundamental for investigation of qualitative theory and numerical interpretation. We derive some necessary results for the existence, uniqueness and various form of Hyers-Ulam (H-U) type stability for the considered problem. For the required results, we need to utilize usual classical fixed point theorems due to Banach and Krasnoselskii's. Moreover, results devoted to H-U stability are derived by using classical tools of nonlinear functional analysis. Some pertinent test problems are given to demonstrate our results.

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