The Analytic Solution of Time-Space Fractional Diffusion Equation via New Inner Product with Weighted Function

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Çetinkaya S., Demir A.

COMMUNICATIONS IN MATHEMATICS AND APPLICATIONS, vol.10, pp.865-873, 2019 (ESCI) identifier

  • Publication Type: Article / Article
  • Volume: 10
  • Publication Date: 2019
  • Doi Number: 10.26713/cma.v10i4.1290
  • Journal Name: COMMUNICATIONS IN MATHEMATICS AND APPLICATIONS
  • Journal Indexes: Emerging Sources Citation Index (ESCI)
  • Page Numbers: pp.865-873
  • Keywords: Caputo fractional derivative, Space-fractional diffusion equation, Mittag-Leffler function, Initial-boundary-value problems, Spectral method, PARTIAL-DIFFERENTIAL-EQUATIONS, BOUNDARY-VALUE PROBLEMS
  • Kocaeli University Affiliated: Yes

Abstract

In this research, we determine the analytic solution of initial boundary value problem including time-space fractional differential equation with Dirichlet boundary conditions in one dimension. By using separation of variables 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 Caputo sense. A new inner product with weighted function is defined to obtain coefficients in the Fourier series.