Existence uniqueness of mild solutions for ψ-Caputo fractional stochastic evolution equations driven by fBm

Abstract

Abstract In this paper, we investigate the existence uniqueness of mild solutions for a class of ψ-Caputo fractional stochastic evolution equations with varying-time delay driven by fBm, which seems to be the first theoretical result of the ψ-Caputo fractional stochastic evolution equations. Alternative conditions to guarantee the existence uniqueness of mild solutions are obtained using fractional calculus, stochastic analysis, fixed point technique, and noncompact measure method. Moreover, an example is presented to illustrate the effectiveness and feasibility of the obtained abstract results.

Keywords

• ψ-Caputo fractional derivative
• Stochastic evolution equations
• Noncompact measure
• Fractional Brownian motion