Implicit type impulsive differential equation analysis with coupled switched system

Abstract

In certain situation many phenomena experiences instantaneous changes. In order to address as well as model such kind of phenomena the unification of switched system with impulsive effects, coupling structures and fractional differential equations is more suitable. Therefore, the present manuscript will initially formulate a general model with coupled switch system having fractional derivative and impulsive effect. Subsequently, will study the existence, uniqueness and stability for the solutions of the formulated system of switched coupled fractional differential equations supplemented with impulsive type boundary conditions. We begin with constructing an integral operator from the given set of differential equations. The main results are obtained by utilising fixed point approach for this integral operator. Thus the existence of unique solution is proved by using classical Banach contraction mapping principle while an existence result is established via Schauder fixed point theorem. Furthermore, Hyers-Ulam stability criteria is embraced to analyse the stability of the solution for the considered problem. Finally our results are well illustrated by numerical application with different cases.