Sequential time space fractional diffusion equation including nonhomogenous initial boundary conditions

In this research, we discuss the construction of analytic solution of non-homogenous initial boundary value problem including PDEs of fractional order. By means of separation of variables method, the solution is constructed in the form of a Fourier series with respect to the eigenfunctions of a corresponding Sturm-Liouville eigenvalue problem including fractional derivative in Liouville-Caputo sense.