Well-posedness for fractional Hardy-H\'enon parabolic equations with fractional Brownian noise

We investigate the fractional Hardy-H\'enon equation with fractional Brownian noise ∂ₜ u(t)+(-Δ)θ/2 u(t)=|x|-γ |u(t)|ᵖ⁻¹u(t)+μ ∂ₜ BH(t), where θ>0, $p>1$, γ≥ 0, μ, and the random forcing BH is the fractional Brownian motion defined on some complete probability space (Ω, F, P) with Hurst parameter H∈ (0,1). We obtain the local existence and uniqueness of mild solutions under tailored conditions on the parameters of the equation.