On the well-posedness of a certain model with mixed diffusion appearing in the mathematical biology

The work deals with establishing the global well-posedness in the space $W^{(1,2),2}(R^{2}\times R^{+})$ of the integro-differential equation in the space of two dimensions in the situation when the diffusion term involves the standard Laplace operator in one direction and the fractional Laplacian in another direction in the presence of the drift term. Such model is relevant to the cell population dynamics in the Mathematical Biology. The proof is based on a fixed point technique.