Hilfer fractional stochastic evolution equations on the positive semi-axis

The focus of this article lies in the existence of global mild solutions for Hilfer fractional stochastic evolution equations (HFSEEs) on the positive semi-axis (0,+∞) with a derivative order greater than 32 and less than 2. A significant challenge, which also presents novelty here, is to extend the generalized Ascoli–Arzela (A–A) theorem established in Zhou and He (2022) to the stochastic case under the associated sine family {S(t)}t≥0 not necessary compact. Then, by relying on our newly established generalized A–A theorem, standard stochastic analysis theory and Schauder’s fixed point principle, we derive the existence of global mild solutions for the addressed system. Finally, we demonstrate the feasibility of our obtained results through an illustrative example.