Time Fractional Diffusion Equation with Periodic Boundary Conditions

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

References

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