Relative controllability for ψ−Caputo fractional delay control system

Abstract

This paper resolves around relative controllability of $\psi -$fractional delayed differential equations in finite dimensional space. The Mittag Leffler type of $\psi -$delayed perturbation matrix function with two parameters exhibits the Grammian matrix of fractional delay system. Based on this Grammian matrix we derived the necessary and sufficient conditions for the linear system which is relatively controllable. The fixed point approach is applied for obtaining a controllability result for semilinear system. This concept can be applied to some examples in order to illustrate the efficacy of our results.