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


Çetinkaya S. , Demir A.

Journal of Scientific Reports-A, vol.45, pp.101-110, 2020 (Refereed Journals of Other Institutions)

  • Publication Type: Article / Article
  • Volume: 45
  • Publication Date: 2020
  • Title of Journal : Journal of Scientific Reports-A
  • Page Numbers: pp.101-110

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 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.