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

We prove the existence and uniqueness of a mild solution for a class of nonautonomous parabolic mixed stochastic partial differential equations defined on a bounded open subset D ⊂ Rd and involving standard and fractional L2(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.