DIFFUSION EQUATION INCLUDING LOCAL FRACTIONAL DERIVATIVE AND NON-HOMOGENOUS DIRICHLET BOUNDARY CONDITIONS
Journal of Scientific Reports-A , sa.45, ss.101-110, 2020 (TRDizin)
- Yayın Türü: Makale / Tam Makale
- Basım Tarihi: 2020
- Dergi Adı: Journal of Scientific Reports-A
- Derginin Tarandığı İndeksler: TR DİZİN (ULAKBİM)
- Sayfa Sayıları: ss.101-110
- Açık Arşiv Koleksiyonu: AVESİS Açık Erişim Koleksiyonu
- Kocaeli Üniversitesi Adresli: Evet
Özet
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 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 local fractional derivative used in this study. Illustrative example
presents the applicability and influence of separation of variables method on fractional mathematical
problems.