The Analytic Solution of Time-Space Fractional Diffusion Equation via New Inner Product with Weighted Function

Authors

  • Süleyman í‡etinkaya Department of Mathematics, Kocaeli University, Kocaeli
  • Ali Demir Department of Mathematics, Kocaeli University, Kocaeli

DOI:

https://doi.org/10.26713/cma.v10i4.1290

Keywords:

Caputo fractional derivative, Space-fractional diffusion equation, Mittag-Leffler function, Initial-boundary-value problems, Spectral method

Abstract

In this research, we determine the analytic solution of initial boundary value problem including time-space fractional differential equation with Dirichlet boundary conditions in one dimension. By using separation of variables 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 Caputo sense. A new inner product with weighted function is defined to obtain coefficients in the Fourier series.

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References

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Published

31-12-2019
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How to Cite

í‡etinkaya, S., & Demir, A. (2019). The Analytic Solution of Time-Space Fractional Diffusion Equation via New Inner Product with Weighted Function. Communications in Mathematics and Applications, 10(4), 865–873. https://doi.org/10.26713/cma.v10i4.1290

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Research Article