A Spectral Collocation Method for Solving the Non-Linear Distributed-Order Fractional Bagley–Torvik Differential Equation

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Amin A. Z. M. A., Abdelkawy M. A., Solouma E., Al-Dayel I.

Fractal and Fractional, vol.7, no.11, 2023 (SCI-Expanded) identifier

  • Publication Type: Article / Article
  • Volume: 7 Issue: 11
  • Publication Date: 2023
  • Doi Number: 10.3390/fractalfract7110780
  • Journal Name: Fractal and Fractional
  • Journal Indexes: Science Citation Index Expanded (SCI-EXPANDED), Scopus, Academic Search Premier, INSPEC, Directory of Open Access Journals
  • Keywords: Caputo fractional derivative, fractional Bagley–Torvik differential equation, shifted Legendre polynomials, spectral collocation method
  • Istanbul Gelisim University Affiliated: No

Abstract

One of the issues in numerical solution analysis is the non-linear distributed-order fractional Bagley–Torvik differential equation (DO-FBTE) with boundary and initial conditions. We solve the problem by proposing a numerical solution based on the shifted Legendre Gauss–Lobatto (SL-GL) collocation technique. The solution of the DO-FBTE is approximated by a truncated series of shifted Legendre polynomials, and the SL-GL collocation points are employed as interpolation nodes. At the SL-GL quadrature points, the residuals are computed. The DO-FBTE is transformed into a system of algebraic equations that can be solved using any conventional method. A set of numerical examples is used to verify the proposed scheme’s accuracy and compare it to existing findings.