Investigation on the Approximate Controllability of Fractional Differential Systems with State Delay

In this article, we presented some sufficient conditions for the approximate controllability of a class of fractional differential systems with fixed delay in Banach space. The existence of a mild solution is discussed with the help of the fixed point theorem. Controllability results are obtained using generalized Gronwall’s inequality, Cauchy sequence, and the basics of functional analysis. As a last note, we have included an example for the illustration of the obtained theory.