The inhomogeneous fractional stochastic heat equation driven by fractional Brownian motion

Purpose The primary objective of this paper is to address a fractional Hardy-Hénon equation driven by fractional Brownian noise. By imposing appropriate conditions on the equation’s parameters, a local well-posedness result has been successfully demonstrated. Design/methodology/approach The authors demonstrate the local existence of a mild solution through the utilization of an associated integral equation. The proof crucially relies on the Banach fixed-point theorem, applied within a carefully chosen complete metric space. Findings The main result of this study is achieving local well-posedness by carefully selecting the parameters of the equation. Originality/value The paper builds upon existing research on similar equations without fractional noise, extending the analysis to include the effects of fractional Brownian motion. This extension contributes to the advancement of knowledge in the field of stochastic partial differential equations.