Trajectory controllability of higher-order Riemann-Liouville fractional stochastic systems via integral contractors in a new Banach space

In this article, we investigate the existence, uniqueness, and trajectory controllability of mild solutions to the fractional stochastic differential system in the new Banach space setting. The results are illustrated by pairing the stochastic process and sequencing technique with the concept of bounded integral contractors. This piece stands out from the earlier ones because it doesn't require the necessary Lipschitz condition for nonlinear functions to satisfy it, nor does it demand an explanation of the results obtained from the induced inverse of the controllability operator. Furthermore, controllability in the sense of trajectory for higher-order Riemann-Liouville stochastic differential systems is demonstrated. An application followed by the theory is displayed at the end. This paper extends all previous works in this direction. Chalishajar et al. [12] and Renu Chaudhary et al. [11] have already been expanded upon by our study.