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

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