Time Fractional Equation with Non-homogenous Dirichlet Boundary Conditions

Authors : Süleyman ÇETİNKAYA, Ali DEMİR

Pages : 1185-1190

Doi:10.16984/saufenbilder.749168

View : 29 | Download : 1

Publication Date : 2020-12-01

Article Type : Research Paper

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 L^2 [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