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 (ESCI) identifier identifier

  • Publication Type: Article / Article
  • Volume: 14 Issue: 7
  • Publication Date: 2021
  • Doi Number: 10.1142/s1793557121501217
  • Journal Name: ASIAN-EUROPEAN JOURNAL OF MATHEMATICS
  • Journal Indexes: Emerging Sources Citation Index (ESCI), Scopus, zbMATH
  • Keywords: Caputo fractional derivative, space fractional diffusion equation, Mittag-Leffler function, initial boundary conditions, spectral method, ANALYTIC SOLUTION
  • Kocaeli University Affiliated: Yes

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.