Controllability of damped dynamical systems modelled by Hilfer fractional derivatives

In this article, we investigate the controllability of damped dynamical system modelled by Hilfer derivative of fractional order tau(1) & ISIN; (1, 2] and tau(2) & ISIN; (0, 1]. The Mittag-Leffler matrix function of two parameters has been used to represent the solution of Hilfer fractional problem of damped dynamical system. With the use of the Schawder fixed point theorem and the contraction mapping theorem, the existence and uniqueness of the linear and non-linear system of Hilfer dynamical control system are determined. More specifically, fractional calculus are used to provide sufficient criteria for the controllability results. Finally, examples are given to show how the key results might be justified.