Fractional Diffusion with Time-Dependent Diffusion Coefficient

In this paper we propose and discuss the fractional diffusion equation with time-dependent diffusion coefficient, considering the Hilfer-type and Weyl fractional derivatives in the time-variable and space-variable, respectively. We apply the similarity method and Mellin transform methodology to find an explicit solution in terms of Fox H-function. We illustrate graphically the diffusive behaviour described by memory and distance effects. We also recover the classical integer order solution as a particular case.