Investigation on the Controllability of Semilinear Integrodifferential Fractional Stochastic Control System in Conformable Sense With Impulses

Controllability concepts have been essential across various disciplines, including control theory, engineering, and applied mathematics. According to Kalman’s definition, controllability points to the capacity to move a control system’s solution from any initial state to a desired state by a predetermined terminal time. In this article, the authors investigate the issue of exact controllability in nonlinear impulsive fractional stochastic systems, assuming that the corresponding linear system is exactly controllable. By applying contraction mapping principle and appropriate conditions on Gramian stochastic controllability operator, the authors establish and demonstrate sufficient conditions for exact controllability. The practical relevance of the derived theoretical findings is demonstrated on a representative example.