Sequential space fractional diffusion equation's solutions via new inner product

ÇETİNKAYA S. , DEMİR A.

ASIAN-EUROPEAN JOURNAL OF MATHEMATICS, vol.14, no.7, 2021 (Journal Indexed in ESCI) identifier identifier

  • Publication Type: Article / Article
  • Volume: 14 Issue: 7
  • Publication Date: 2021
  • Doi Number: 10.1142/s1793557121501217
  • Title of Journal : ASIAN-EUROPEAN JOURNAL OF MATHEMATICS
  • Keywords: Caputo fractional derivative, space fractional diffusion equation, Mittag-Leffler function, initial boundary conditions, spectral method, ANALYTIC SOLUTION

Abstract

In this study, we determine the analytic solutions of sequential space fractional differential equations with Dirichlet boundary conditions and initial conditions in one dimension. We constructed a Fourier series solution for the eigenfunctions of a corresponding Sturm-Liouville eigenvalue problem, including fractional derivative in Caputo sense using the separation of variables. We defined a new inner product with a weighted function to get coefficients in the Fourier series.