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We prove existence and uniqueness of the solution for a class of mixedfractional stochastic differential equations with discontinuous drift driven byboth standard and fractional Brownian motion. Additionally, we establish ageneralized It\^o rule valid for functions with absolutely continuousderivative and applicable to solutions of mixed fractional stochasticdifferential equations with Lipschitz coefficients, which plays a key role inour proof of existence and uniqueness. The proof of such a formula is new andrelies on showing the existence of a density of the law under mild assumptionson the diffusion coefficient.

On mixed fractional SDEs with discontinuous drift coefficient