In this paper, we define the mixed fractional Constant Elasticity of Variance (CEV) process exploiting a transfer equation. This transformation enables us to shift non-linearity from the volatility coefficient into the drift one and accordingly, the problem can be more easily studied. We confirm the existence of a unique positive solution to the transfer equation and verify the conditions under which the probability that, on any fixed finite interval, the mixed fractional CEV process does not hit zero tends to 1 (by some simulation, we illustrate more). Next, some parameters of the process are estimated and finally, we examine the ability of this process to model a financial market.