Nonlinear integro-differential equations with small unknown parameters: A controllability analysis problem

This manuscript is perturbed with a controllability problem of nonlinear fractional dynamical systems with delay in the state variable. By employing Laplace transformation technique and using Mittag-Leffler function, solution representation of the examined fractional delay differential equations can be devised. Besides, we build the necessary as well as sufficient condition, in order to prove the controllability of linear fractional delay dynamical structures. Especially, the sufficiency part for the controllability results is obtained by using the fixed point argument. In addition to that, we have provided three numerical examples to illustrate the essence of our obtained theoretical statements.