Approximate and Exact Controllability for Hilfer Fractional Stochastic Evolution Equations

This paper investigates the controllability of Hilfer fractional stochastic evolution equations (HFSEEs). Initially, we obtain a conclusion regarding the approximate controllability of HFSEEs by employing the Tikhonov-type regularization method and Schauder′s fixed-point theorem. Additionally, the conditions for the exact controllability of HFSEEs are explored, utilizing the Mönch′s fixed-point theorem and measure of noncompactness. Finally, the proposed method is validated through an example, thereby demonstrating its effectiveness.