DIFFUSION EQUATION INCLUDING LOCAL FRACTIONAL DERIVATIVE AND NON-HOMOGENOUS DIRICHLET BOUNDARY CONDITIONS

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Çetinkaya S., Demir A.

Journal of Scientific Reports-A , sa.45, ss.101-110, 2020 (Hakemli Dergi)

  • 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
  • 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.