On a nonlinear neutral stochastic functional integro-differential equation driven by fractional Brownian motion

TL;DR

This paper investigates the existence, uniqueness, and density of solutions for a complex stochastic neutral integro-differential equation driven by fractional Brownian motion, with applications demonstrated through an example.

Contribution

It introduces new conditions for solution existence and density in fractional Brownian motion-driven equations with delay in a Hilbert space.

Findings

Proved existence and uniqueness of mild solutions.

Established conditions for the solution's density.

Provided an illustrative example.

Abstract

In this paper, we study the existence and uniqueness of mild solution for a stochastic neutral partial functional integro-differential equation with delay in a Hilbert space driven by a fractional Brownian motion and with non-deterministic diffusion coefficient. We suppose that the linear part has a resolvent operator. We also establish a sufficient condition for the existence of the density of a function of the solution. An example is provided to illustrate the results of this work