The Analytic Solution of Initial Periodic Boundary Value Problem Including Sequential Time Fractional Diffusion Equation - Cetinkaya, Suleyman; Demir, Ali; Sevindir, Hülya Kodal (Communications in Mathematics and Applications, 2020)
In this study, the separation of variables method is applied to form the analytic solution of periodic boundary value problem including time fractional differential equation with periodic boundary conditions in one dimension. The solution is obtained in the form of a Fourier series with respect to the eigenfunctions of a corresponding Sturm-Liouville eigenvalue problem.
Keywords: Caputo fractional derivative; Space-fractional diffusion equation; Mittag-Leffler function; Periodic-boundary-value problems; Spectral method