The Existence of Mild Solutions for Hilfer Fractional Stochastic Evolution Equations with Order <i>μ</i>∈(1,2)

Abstract

In this study, we investigate the existence of mild solutions for a class of Hilfer fractional stochastic evolution equations with order μ∈(1,2) and type ν∈[0,1]. We prove the existence of mild solutions of Hilfer fractional stochastic evolution equations when the semigroup is compact as well as noncompact. Our approach is based on the Schauder fixed point theorem, the Ascoli–Arzelà theorem and the Kuratowski measure of noncompactness. An example is also provided, to demonstrate the efficacy of this method.

Keywords

• stochastic evolution equation
• Hilfer fractional derivative
• mild solution