Time Fractional Equation Including Non-homogenous Dirichlet Boundary Conditions

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Çetinkaya S., Demir A.

Sakarya University Journal of Science, cilt.6, sa.24, ss.1185-1190, 2020 (Hakemli Dergi)

  • 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
  • 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.