Diffusion Equation Including Local Fractional Derivative and Dirichlet Boundary Conditions

ÇETİNKAYA S., DEMİR A.

Konuralp Journal of Mathematics, cilt.11, sa.2, ss.148-154, 2023 (Scopus) identifier

  • Yayın Türü: Makale / Tam Makale
  • Cilt numarası: 11 Sayı: 2
  • Basım Tarihi: 2023
  • Dergi Adı: Konuralp Journal of Mathematics
  • Derginin Tarandığı İndeksler: Scopus
  • Sayfa Sayıları: ss.148-154
  • Anahtar Kelimeler: Dirichlet boundary conditions, Local Fractional Derivative, Separation of variables, Spectral method
  • Kocaeli Üniversitesi Adresli: Evet

Özet

In this research, we discuss the construction of analytic solution of homogenous initial boundary value problem including PDEs of fractional order. Since homogenous initial boundary value problem involves local fractional order derivative, it has classical initial and boundary conditions. By means of separation of variables method and the inner product defined on L2 [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 local sense used in this study. Illustrative example presents the applicability and influence of separation of variables method on fractional mathematical problems.