On the Asymptotic Stability of Hilfer Fractional Neutral Stochastic Differential Systems with Infinite Delay

This article explores the existence and asymptotic stability in the p-th moment of mild solutions to a class of Hilfer fractional neutral stochastic differential equations with infinite delay in Hilbert spaces. To prove our main results, we use fractional calculus, stochastic analysis, semigroup theory, and the Krasnoselskii-Schaefer type fixed point theorem. Moreover, a set of novel sufficient conditions is derived for achieving the required result. Following that, we extend the given system to the Sobolev type and provided the existence results of the considered system. After that, we provided an example to illustrate the validity of our results.