A Chebyshev collocation method for solving the non-linear variable-order fractional Bagley-Torvik differential equation

Amin A. Z. M. A., Lopes A. M., Hashim I.

International Journal of Nonlinear Sciences and Numerical Simulation, cilt.24, sa.5, ss.1613-1630, 2023 (SCI-Expanded) identifier

  • Yayın Türü: Makale / Tam Makale
  • Cilt numarası: 24 Sayı: 5
  • Basım Tarihi: 2023
  • Doi Numarası: 10.1515/ijnsns-2021-0395
  • Dergi Adı: International Journal of Nonlinear Sciences and Numerical Simulation
  • Derginin Tarandığı İndeksler: Science Citation Index Expanded (SCI-EXPANDED), Scopus, Academic Search Premier, Aerospace Database, Communication Abstracts, INSPEC, Metadex, zbMATH, Civil Engineering Abstracts
  • Sayfa Sayıları: ss.1613-1630
  • Anahtar Kelimeler: Caputo fractional derivative of variable order, fractional Bagley-Torvik differential equation, shifted Chebyshev polynomials, spectral collocation method
  • İstanbul Gelişim Üniversitesi Adresli: Hayır

Özet

A numerical approach based on the shifted Chebyshev-Gauss collocation method is proposed for solving the non-linear variable-order fractional Bagley-Torvik differential equation (VO-FBTE), subject to initial and boundary conditions. The shifted fractional Chebyshev-Gauss collocation points are used as interpolation nodes, and the solution of the VO-FBTE is approximated by a truncated series of the shifted Chebyshev polynomials. The residuals are calculated at the shifted fractional Chebyshev-Gauss quadrature points. The original VO-FBTE is converted into a system of algebraic equations. The accuracy of the proposed scheme is confirmed with a set of numerical examples, and the results are compared with those obtained by other methods.