Time Fractional Diffusion Equation with Periodic Boundary Conditions

Authors : Süleyman ÇETİNKAYA, Ali DEMİR

Pages : 337-342

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Publication Date : 2020-10-27

Article Type : Research Paper

Abstract :The aim of this research is to establish the analytic solution of time fractional diffusion equations with periodic boundary conditions in one dimension by implementing well-known separation of variables method. First, the eigenvalues of the obtained Sturm-Liouville problem are determined by investigating all cases. The corresponding eigenfunctions are obtained in the second step. Utilizing eigenvalues and eigenfunctions, the Fourier series of the solution is constructed in terms of Mittag-Leffler function and the coefficients are computed by taking $L^2$ inner product and initial condition into account at the final step.
Keywords : Caputo fractional derivative, Mittag Leffler function, Periodic boundary conditions, Spectral method, Time fractional diffusion equation