Controllability of time-varying fractional dynamical systems

The aim of this article is to investigate the controllability results for the time-varying fractional dynamical systems with the presence of the Caputo-type fractional derivative. The Bourdin state transition matrix is used to form the solution for the time-varying fractional dynamical system. The classical Grammian matrix-based technique is utilized to derive the controllability results for time-varying linear systems, and the controllability of the proposed nonlinear type system is established by utilizing the well-known Arzela-Ascoli theorem and Schauder's fixed point theorem. The main motivation for this study is to develop the controllability results for time-varying fractional dynamical systems represented by the Caputo fractional derivative. Several numerical examples are provided to validate and illustrate the applicability of the theoretical results.