Diffusion Equation Including Local Fractional Derivatıve and Non-Homogenous Dirichlet Boundary Conditions

Çetinkaya S., Demir A.

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

  • Yayın Türü: Makale / Tam Makale
  • Cilt numarası: 45
  • Basım Tarihi: 2020
  • Dergi Adı: Journal of Scientific Reports-A
  • 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.