This article investigates controllability results for fractional dynamical systems with prescribed control, formulated using the (Formula presented.) -Caputo type fractional derivative. For linear systems, controllability is established via fractional calculus and the Gramian approach, while for nonlinear systems it is examined using Krasnoselskii’s fixed point technique. Theoretical findings are further supported with illustrative numerical examples. The study also discusses the mathematical framework required for the analysis and highlights the logical steps followed to derive the main results.