Analytical solution of the space-time fractional reaction-diffusion equation with variable coefficients

In this paper, we solve the problem of an inhomogeneous one-dimensional fractional differential reaction-diffusion equation with variable coefficients (1.1)-(1.2) by the method of separation of variables (the Fourier method). The Caputo derivative and the Riemann-Liouville derivative are considered in the time and space directions, respectively. We prove that the obtained solution of the boundary-value problem satisfies the given boundary conditions. We discuss the convergence of the series defining the proposed solution.