Controllability Analysis of Impulsive Multi-Term Fractional-Order Stochastic Systems Involving State-Dependent Delay

Abstract

This study deals with the controllability of multi-term fractional-order stochastic systems with impulsive effects and state-dependent delay that exhibit damping behavior. Based on fractional calculus theory, the Caputo fractional derivative is utilized to analyze the controllability of fractional-order systems. Mittag–Leffler functions and Laplace transform are used to derive the solution set of the problem. Sufficient conditions for the controllability of nonlinear systems are achieved using fixed-point techniques and stochastic theory. Finally, the results stated in the paper are validated using examples.