The construction of operational matrix of fractional derivatives using B-spline functions

Lakestanı M., Dehghan M., Irandoust-pakchin S.

Communications in Nonlinear Science and Numerical Simulation, cilt.17, sa.3, ss.1149-1162, 2012 (SCI-Expanded) identifier

  • Yayın Türü: Makale / Tam Makale
  • Cilt numarası: 17 Sayı: 3
  • Basım Tarihi: 2012
  • Doi Numarası: 10.1016/j.cnsns.2011.07.018
  • Dergi Adı: Communications in Nonlinear Science and Numerical Simulation
  • Derginin Tarandığı İndeksler: Science Citation Index Expanded (SCI-EXPANDED), Scopus
  • Sayfa Sayıları: ss.1149-1162
  • Anahtar Kelimeler: B-spline function, Caputo derivative, Operational matrix of fractional derivative
  • Van Yüzüncü Yıl Üniversitesi Adresli: Evet

Özet

Fractional calculus has been used to model physical and engineering processes that are found to be best described by fractional differential equations. For that reason we need a reliable and efficient technique for the solution of fractional differential equations. Here we construct the operational matrix of fractional derivative of order α in the Caputo sense using the linear B-spline functions. The main characteristic behind the approach using this technique is that it reduces such problems to those of solving a system of algebraic equations thus we can solve directly the problem. The method is applied to solve two types of fractional differential equations, linear and nonlinear. Illustrative examples are included to demonstrate the validity and applicability of the new technique presented in the current paper. © 2011 Elsevier B.V.