Study on Controllability for Ψ-Hilfer Fractional Stochastic Differential Equations - Abdur Raheem; Fahad M. Alamrani; Javed Akhtar; Adel Alatawi; Esmail Alshaban; Areefa Khatoon; Faizan Ahmad Khan (Fractal and Fractional)
The goal of this paper is to study the existence of a mild solution and controllability for a class of neutral stochastic differential equations (SDEs) involving the <semantics>Ψ</semantics>-Hilfer fractional derivatives, a generalization of the well-known Riemann–Liouville fractional derivative using almost sectorial operators. Sufficient conditions for controllability are established using the notion of measure of noncompactness (MNC) and the Mönch fixed-point theorem. An example is given to illustrate the abstract findings.