A Study on Approximate Controllability of Ψ-Caputo Fractional Differential Equations with Impulsive Effects

Abstract

In this article, we studied the approximate controllability of Ψ-Caputo fractional differential systems. We prove the sufficient conditions for an abstract Cauchy problem invloving infinite delay, impulsive and nonlocal conditions. The result is shown by means of the infinitesimal operator, semigroup theory, fractional calculus, and Schauder’s fixed point theorem. First, we prove the existence of the mild solution and demonstrate that the Ψ-Caputo fractional system is approximately controllable. Finally, an example is given to analyse the obtained results.