Mathematical analysis of the Cauchy type dynamical system under piecewise equations with Caputo fractional derivative

Kamal Shah, Thabet Abdeljawad and Arshad Ali

Chaos, Solitons & Fractals, 2022, vol. 161, issue C

Abstract: This research work is related to study the Cauchy type dynamical system under piecewise equations with fractional order Caputo derivative. Using traditional fixed point tools due to Banach and Schauder, the required results for the existence and uniqueness are developed. Since stability analysis is an important aspect of the aforesaid analysis, so we also attempt on Hyers-Ulam (HU) type stability results for the proposed system. For this purposes, we use tools of nonlinear functional analysis. Further a numerical method based on Newton polynomials of interpolation is applied to compute approximate solution for the considered system. For application and validity purpose of our main results, we give two illustrative examples.

Keywords: Piecewise Caputo derivative; Existence theory; Stability result; Newton polynomials; Numerical result (search for similar items in EconPapers)
Date: 2022
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Citations: View citations in EconPapers (1)

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Persistent link: https://EconPapers.repec.org/RePEc:eee:chsofr:v:161:y:2022:i:c:s0960077922005665

DOI: 10.1016/j.chaos.2022.112356

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