Existence and uniqueness of an attractive nonlinear diffusion system

We establish the existence and uniqueness of an attractive fractional coupled system. Such a system has applications in biological populations of cells. We confirm that the fractional system under consideration admits a global solution in the Sobolev space. The solution is shown to be unique. The technique is founded on analytic method of the fixed point theory and the fractional differential operator is scrutinized from the view of the Riemann-Liouville differential operator. Finally, we illustrate some entropy fractional differential inequalities regarding the solution of the system.