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

This research work is related to study the Cauchy type dynamical system under piecewise equations with frac-tional order Caputo derivative. Using traditional fixed point tools due to Banach and Schauder, the required re-sults 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 (H\\U) 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 applica-tion and validity purpose of our main results, we give two illustrative examples.(c) 2022 Elsevier Ltd. All rights reserved.