A study on controllability of fractional dynamical systems with distributed delays modeled by Ω -Hilfer fractional derivatives

This paper deals with the controllability of fractional dynamical systems with distributed delays modeled by Omega-Hilfer fractional derivatives. Firstly, the Q-Hilfer fractional problem is defined and solution representation of x(t) with the help of Laplace transform, Mittag-leffler function is obtained. Furthermore, the controllability of linear system is achieved based on controllability Grammarian matrix and rank matrix criteria. Moreover, to study the nonlinear system, theorem of schauder's fixed point of continuous function is satisfied. Then, both the system should be controllable for the Omega-Hilfer fractional derivatives. Finally, two numerical examples are discussed to support the controllability Grammarian matrix results.