Controllability for ψ-Hilfer fractional Sobolev-type stochastic differential system

In this article, we explore the existence and controllability results for a class of ψ -Hilfer fractional Sobolev-type stochastic differential systems with infinite delay. Sufficient conditions for controllability results are obtained by using the notion of the measure of noncompactness, stochastic theory, fractional calculus, and the Mönch fixed point theorem. A key feature of our work is the use of the ψ -Hilfer fractional derivative (FD), which provides a unified framework by generalizing several well-known fractional operators, including the Hilfer, Caputo, and Riemann–Liouville(R-L) derivatives. This flexibility makes our approach particularly effective for capturing memory effects and improving the modeling accuracy of real-world dynamical systems. Finally, we present a concrete example to demonstrate the applicability of our theoretical findings.