Trajectory Controllability of Fractional Neutral Stochastic Dynamical Systems of Order α∈1,2 With Deviating Argument

In this manuscript, we establish existence, uniqueness, and trajectory controllability for higher order noninstantaneous impulsive fractional neutral stochastic differential equations. First, solvability and uniqueness results are obtained using a fixed-point approach with appropriate assumptions on nonlinear functions. Next, we deal with the strongest notion of controllability called the trajectory controllability for noninstantaneous impulsive fractional neutral stochastic differential equations via Gronwall’s inequality. The higher order fractional system with the deviating argument is the novel approach of this manuscript. Finally, a demonstration of an example yields theoretical outcomes.