On $L_p$-solution of fractional heat equation driven by fractional Brownian motion

In this paper, we study the fractional stochastic heat equation driven by fractional Brownian motions of the form$$du(t,x)=left(-(-Delta)^{alpha/2}u(t,x)+f(t,x)right)dt +sumlimits^{infty}_{k=1} g^k(t,x)deltabeta^k_t$$with $u(0,x)=u_0$, $tin[0,T]$ and $xinmathbb{R}^d$, where $beta^k={beta^k_t,tin[0,T]},kgeq1$ is a sequence of i.i.d. fractional Brownian motions with the same Hurst index $H>1/2$ and the integral with respect to fractional Brownian motion is Skorohod integral. By adopting the framework given by Krylov, we prove the existence and uniqueness of $L_p$-solution to such equation.