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

Abstract

In this research, we discuss the construction of analytic solution of non-homogenous initial boundaryvalue problem including PDEs of fractional order. Since non-homogenous initial boundary valueproblem involves local fractional derivative, it has classical initial and boundary conditions. By meansof separation of variables method and the inner product defined on 𝐿2[0,𝑙], the solution is constructedin the form of a Fourier series with respect to the eigenfunctions of a corresponding Sturm-Liouvilleeigenvalue problem including local fractional derivative used in this study. Illustrative examplepresents the applicability and influence of separation of variables method on fractional mathematicalproblems.