  In the article we establish the global well-posedness in W^{1, 2, 2}(R\times
R^{+}) of the integro-differential equation in the case of the anomalous
diffusion when the one dimensional negative Laplace operator is raised to a
fractional power in the presence of the transport term. The model is relevant
to the cell population dynamics in the Mathematical Biology. Our proof relies
on a fixed point technique.
