A Galerkin-Type Fractional Approach for Solutions of Bagley-Torvik Equations

YÜZBAŞI Ş., KARAÇAYIR M.

CMES-COMPUTER MODELING IN ENGINEERING & SCIENCES, cilt.123, sa.3, ss.941-956, 2020 (SCI-Expanded) identifier identifier

  • Yayın Türü: Makale / Tam Makale
  • Cilt numarası: 123 Sayı: 3
  • Basım Tarihi: 2020
  • Doi Numarası: 10.32604/cmes.2020.08938
  • Dergi Adı: CMES-COMPUTER MODELING IN ENGINEERING & SCIENCES
  • Derginin Tarandığı İndeksler: Science Citation Index Expanded (SCI-EXPANDED), Scopus, Aerospace Database, Communication Abstracts, Compendex, INSPEC, Metadex, zbMATH, Civil Engineering Abstracts
  • Sayfa Sayıları: ss.941-956
  • Anahtar Kelimeler: Bagley-Torvik equation, fractional derivative, Galerkin method, numerical solutions, CALCULUS
  • Akdeniz Üniversitesi Adresli: Evet

Özet

In this study, we present a numerical scheme similar to the Galerkin method in order to obtain numerical solutions of the Bagley Torvik equation of fractional order 3/2. In this approach, the approximate solution is assumed to have the form of a polynomial in the variable t = x(alpha), where alpha is a positive real parameter of our choice. The problem is firstly expressed in vectoral form via substituting the matrix counterparts of the terms present in the equation. After taking inner product of this vector with nonnegative integer powers of t up to a selected positive parameter N, a set of linear algebraic equations is obtained. After incorporation of the boundary conditions, the approximate solution of the problem is then computed from the solution of this linear system. The present method is illustrated with two examples.