- Sakarya Üniversitesi Fen Bilimleri Enstitüsü Dergisi
- Vol: 24 Issue: 6
- Time Fractional Equation with Non-homogenous Dirichlet Boundary Conditions
Time Fractional Equation with Non-homogenous Dirichlet Boundary Conditions
Authors : Süleyman Çetinkaya, Ali Demir
Pages : 1185-1190
Doi:10.16984/saufenbilder.749168
View : 30 | Download : 0
Publication Date : 2020-12-01
Article Type : Other
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