Numerical solution of the Bagley-Torvik equation by the Bessel collocation method

YÜZBAŞI Ş.

MATHEMATICAL METHODS IN THE APPLIED SCIENCES, vol.36, no.3, pp.300-312, 2013 (SCI-Expanded) identifier identifier

  • Publication Type: Article / Article
  • Volume: 36 Issue: 3
  • Publication Date: 2013
  • Doi Number: 10.1002/mma.2588
  • Journal Name: MATHEMATICAL METHODS IN THE APPLIED SCIENCES
  • Journal Indexes: Science Citation Index Expanded (SCI-EXPANDED), Scopus
  • Page Numbers: pp.300-312
  • Keywords: Bagley-Torvik equation, fractional differential equations, Caputo fractional derivative, Bessel collocation method, Bessel functions of the first kind, FRACTIONAL DIFFERENTIAL-EQUATIONS, INTEGRODIFFERENTIAL EQUATIONS, RESIDUAL CORRECTION, SYSTEMS, CALCULUS, ORDER
  • Akdeniz University Affiliated: Yes

Abstract

In this article, a numerical technique is presented for the approximate solution of the Bagley–Torvik equation, which is a class of fractional differential equations. The basic idea of this method is to obtain the approximate solution in a generalized form of the Bessel functions of the first kind. For this purpose, by using the collocation points, the matrix operations and a generalization of the Bessel functions of the first kind, this technique transforms the Bagley–Torvik equation into a system of the linear algebraic equations. Hence, by solving this system, the unknown Bessel coefficients are computed. The reliability and efficiency of the proposed scheme are demonstrated by some numerical examples.

In this article, a numerical technique is presented for the approximate solution of the BagleyTorvik equation, which is a class of fractional differential equations. The basic idea of this method is to obtain the approximate solution in a generalized form of the Bessel functions of the first kind. For this purpose, by using the collocation points, the matrix operations and a generalization of the Bessel functions of the first kind, this technique transforms the BagleyTorvik equation into a system of the linear algebraic equations. Hence, by solving this system, the unknown Bessel coefficients are computed. The reliability and efficiency of the proposed scheme are demonstrated by some numerical examples. Copyright (c) 2012 John Wiley & Sons, Ltd.