Time Fractional Equation with Non-homogenous Dirichlet Boundary Conditions

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 Caputo fractional order derivative, it has classical initial and boundary conditions. By means of separation of variables method and the inner product defined on 𝐿ଶ[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 fractional derivative in Caputo sense used in this study. Illustrative example presents the applicability and influence of separation of variables method on fractional mathematical problems.Keywords: Caputo fractional derivative, Time-fractional diffusion equation, Mittag-Leffler function, Initial-boundary-value problems, Spectral method.