DIFFUSION EQUATION INCLUDING LOCAL FRACTIONAL DERIVATIVE AND NON-HOMOGENOUS DIRICHLET BOUNDARY CONDITIONS

In this research, we discuss the construction of analytic solution of non-homogenous initial boundary value problem including PDEs of fractional order. Since non-homogenous initial boundary value problem involves local fractional derivative, it has classical initial and boundary conditions. By means of separation of variables method and the inner product defined on ?2[0,?], the solution is constructed in the form of a Fourier series with respect to the eigenfunctions of a corresponding Sturm-Liouville eigenvalue problem including local fractional derivative used in this study. Illustrative example presents the applicability and influence of separation of variables method on fractional mathematical problems.

Keywords:

Local fractional derivative, Time-fractional diffusion equation, Initial-boundary-value problems Spectral method, Non-homogenous Dirichlet boundary conditions,

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Başlangıç: 2020
Yayıncı: Kütahya Dumlupınar Üniversitesi

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