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.
•A Cauchy type dynamical system is considered.•By using Piecewise equation, the model is investigated.•Existence theory is established.•Numerical analysis is done.