Controllability of Hilfer Fractional Semilinear Integro-Differential Equation of Order α ∊ (0, 1), β ∊ [0, 1]

Abstract

In this paper, Hilfer fractional differential equation is studied. Firstly, we used Laplace transform and semigroup theory to find the mild solution of the system. Then exact controllability of proposed system is established using the Arzela-Ascoli theorem and Schauder fixed point theorem. To illustrate the developed theory we provide an example at the end.