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

ÇETİNKAYA S., DEMİR A.

ASIAN-EUROPEAN JOURNAL OF MATHEMATICS, cilt.14, sa.7, 2021 (ESCI) identifier identifier

  • Yayın Türü: Makale / Tam Makale
  • Cilt numarası: 14 Sayı: 7
  • Basım Tarihi: 2021
  • Doi Numarası: 10.1142/s1793557121501217
  • Dergi Adı: ASIAN-EUROPEAN JOURNAL OF MATHEMATICS
  • Derginin Tarandığı İndeksler: Emerging Sources Citation Index (ESCI), Scopus, zbMATH
  • Anahtar Kelimeler: Caputo fractional derivative, space fractional diffusion equation, Mittag-Leffler function, initial boundary conditions, spectral method, ANALYTIC SOLUTION
  • Kocaeli Üniversitesi Adresli: Evet

Özet

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.