Stochastic delay fractional evolution equations driven by fractional Brownian motion

TL;DR

This paper studies a class of stochastic delay fractional evolution equations driven by fractional Brownian motion, establishing conditions for solutions and applying the results to a stochastic fractional heat equation.

Contribution

It provides new sufficient conditions for existence and uniqueness of mild solutions for these complex stochastic equations.

Findings

Established existence and uniqueness of solutions.

Applied theory to a stochastic fractional heat equation.

Provided a framework for analyzing similar stochastic delay equations.

Abstract

In this paper, we consider a class of stochastic delay fractional evolution equations driven by fractional Brownian motion in a Hilbert space. Sufficient conditions for the existence and uniqueness of mild solutions are obtained. An application to the stochastic fractional heat equation is presented to illustrate the theory.