Reachability of time-varying fractional dynamical systems with prescribed control

The focus of this article revolves around investigating reachability results in the context of time-varying fractional dynamical systems with prescribed or predetermined control by employing Riemann-Liouville's fractional derivative. The investigation delves into the necessary and sufficient conditions for reachability results concerning time-varying linear fractional dynamical systems, employing both the Gramian technique and fractional calculus. Additionally, Schauder's fixed-point technique is employed to establish the sufficient conditions for the reachability results of time-varying nonlinear fractional dynamical systems. The validity of the theoretical findings is confirmed through the successive approximation technique, accompanied by a series of numerical examples.