Time Fractional Equation Including Non-homogenous Dirichlet Boundary Conditions


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Çetinkaya S., Demir A.

Sakarya University Journal of Science, vol.6, no.24, pp.1185-1190, 2020 (Peer-Reviewed Journal)

  • Publication Type: Article / Article
  • Volume: 6 Issue: 24
  • Publication Date: 2020
  • Journal Name: Sakarya University Journal of Science
  • Journal Indexes: Academic Search Premier, Business Source Elite, Business Source Premier, Directory of Open Access Journals, TR DİZİN (ULAKBİM)
  • Page Numbers: pp.1185-1190
  • Kocaeli University Affiliated: Yes

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 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.