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

Year 2020, Issue: 045, 101 - 110, 31.12.2020

Süleyman Çetinkaya , Ali Demir

Abstract

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 𝐿2[0,𝑙], 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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