Numerical approach for solving a class of nonlinear fractional differential equations

Irandoust-Pakchin S., Lakestanı M., Kheiri H.

Bulletin of the Iranian Mathematical Society, cilt.42, sa.5, ss.1107-1126, 2016 (SCI-Expanded) identifier

  • Yayın Türü: Makale / Tam Makale
  • Cilt numarası: 42 Sayı: 5
  • Basım Tarihi: 2016
  • Dergi Adı: Bulletin of the Iranian Mathematical Society
  • Derginin Tarandığı İndeksler: Science Citation Index Expanded (SCI-EXPANDED), Scopus
  • Sayfa Sayıları: ss.1107-1126
  • Anahtar Kelimeler: Caputo derivative, Chebyshev cardinal function, Col-location method, Fractional-order differential equation, Operational matrix of fractional derivative
  • Van Yüzüncü Yıl Üniversitesi Adresli: Evet

Özet

It is commonly accepted that fractional differential equations play an important role in the explanation of many physical phenomena. For this reason we need a reliable and efficient technique for the solution of fractional differential equations. This paper deals with the numerical solu- tion of a class of fractional differential equation. The fractional derivatives are described based on the Caputo sense. Our main aim is to generalize the Chebyshev cardinal operational matrix to the fractional calculus. In this work, the Chebyshev cardinal functions together with the Chebyshev cardinal operational matrix of fractional derivatives are used for numerical solution of a class of fractional differential equations. The main advan- tage of this approach is that it reduces fractional problems to a system of algebraic equations. The method is applied to solve nonlinear fractional differential equations. Illustrative examples are included to demonstrate the validity and applicability of the presented technique.