Analyze existence, uniqueness and controllability of impulsive fractional functional differential equations

This manuscript demonstrated the impulsive fractional functional differential equation and established the controllability criterion. By employing Laplace transformation and Mittag-Leffler function, the solution representation was derived and subsequently, one can construct the suitable control function and analyzed the controllability criteria for the given dynamical system. The existence results acquired with some assumptions with Schauder Fixed Point theorem and uniqueness results were attained by Banach Contraction Principle. Eventually, two numerical examples were provided with MATLAB graphical representation for the efficacy of results.