A Study Concerning to the Existence and Averaging Principle for ψ‐Hilfer Fractional Stochastic Evolution Equations

ABSTRACT This paper primarily focuses on a class of ‐Hilfer fractional stochastic evolution equations (FSEEs). First, we establish the existence and uniqueness of mild solutions for the considered system using the Banach contraction principle. Subsequently, with the aid of fractional calculus, stochastic analysis theory, semigroup properties and inequality techniques, we derive the averaging principle and demonstrate that the mild solution of the ‐Hilfer FSEEs converges to that of the reduced averaged equations in terms of mean square sense. Compared to previous usual growth conditions, our modified assumptions presented in this paper are more general and effectively overcome difficulties arising from the flexibility in choosing function . Lastly, we provide an example to illustrate the obtained theoretical results.