Time Fractional Equation Including Non-homogenous Dirichlet Boundary Conditions
Sakarya University Journal of Science, cilt.6, sa.24, ss.1185-1190, 2020 (TRDizin)
- Yayın Türü: Makale / Tam Makale
- Cilt numarası: 6 Sayı: 24
- Basım Tarihi: 2020
- Dergi Adı: Sakarya University Journal of Science
- Derginin Tarandığı İndeksler: Academic Search Premier, Business Source Elite, Business Source Premier, Directory of Open Access Journals, TR DİZİN (ULAKBİM)
- Sayfa Sayıları: ss.1185-1190
- 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 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
ଶ
[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.