The Analytic Solution of Initial Periodic Boundary Value Problem Including Sequential Time Fractional Diffusion Equation

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Çetinkaya S., Demir A., Kodal Sevindir H.

COMMUNICATIONS IN MATHEMATICS AND APPLICATIONS, vol.11, pp.173-179, 2020 (ESCI) identifier

  • Publication Type: Article / Article
  • Volume: 11
  • Publication Date: 2020
  • Doi Number: 10.26713/cma.v11i1.1293
  • Journal Name: COMMUNICATIONS IN MATHEMATICS AND APPLICATIONS
  • Journal Indexes: Emerging Sources Citation Index (ESCI)
  • Page Numbers: pp.173-179
  • Keywords: Caputo fractional derivative, Space-fractional diffusion equation, Mittag-Leffler function, Periodic-boundary-value problems, Spectral method, PARTIAL-DIFFERENTIAL-EQUATIONS, INVERSE PROBLEM
  • Kocaeli University Affiliated: Yes

Abstract

In this study, the separation of variables method is applied to form the analytic solution of periodic boundary value problem including time fractional differential equation with periodic boundary conditions in one dimension. The solution is obtained in the form of a Fourier series with respect to the eigenfunctions of a corresponding Sturm-Liouville eigenvalue problem.