# Existence and uniqueness of mild solution to stochastic heat equation with white and fractional noises

## TL;DR

This paper establishes the existence and uniqueness of mild solutions for a class of stochastic heat equations driven by both white and fractional noises, expanding understanding of such complex stochastic PDEs.

## Contribution

It provides the first proof of existence and uniqueness for non-autonomous stochastic heat equations with mixed white and fractional noises under specified conditions.

## Key findings

- Proved existence and uniqueness of mild solutions.
- Handled equations with fractional Brownian motion.
- Extended results to non-autonomous parabolic SPDEs.

## Abstract

We prove the existence and uniqueness of a mild solution for a class of non-autonomous parabolic mixed stochastic partial differential equations defined on a bounded open subset $D \subset \mathbb{R}^d$ and involving standard and fractional $L^2(D)$-valued Brownian motions. We assume that the coefficients are homogeneous, Lipschitz continuous and the coefficient at the fractional Brownian motion is an affine function.