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

Süleyman Çetinkaya, Ali Demir

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.


Keywords


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

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References


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DOI: http://dx.doi.org/10.26713%2Fcma.v10i4.1290

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