Power Series Method for Linear Partial Differential Equations of Fractional Order

KURULAY M., Bayram M.

COMMUNICATIONS IN MATHEMATICS AND APPLICATIONS, cilt.1, sa.2, ss.71-76, 2010 (ESCI) identifier

  • Yayın Türü: Makale / Tam Makale
  • Cilt numarası: 1 Sayı: 2
  • Basım Tarihi: 2010
  • Dergi Adı: COMMUNICATIONS IN MATHEMATICS AND APPLICATIONS
  • Derginin Tarandığı İndeksler: Emerging Sources Citation Index (ESCI)
  • Sayfa Sayıları: ss.71-76
  • Anahtar Kelimeler: Power series method, Fractional differential equation, Caputo fractional derivative
  • Yıldız Teknik Üniversitesi Adresli: Evet

Özet

In this article, a novel numerical method is proposed for linear partial differential equations with time-fractional derivatives. This method is based on power series and generalized Taylor's formula. The fractional derivatives are considered in the Caputo sense. Several illustrative examples are given to demonstrate the effectiveness of the present method. The modified algorithm provides approximate solutions in the form of convergent series with easily computable components. The obtained results are in good agreement with the existing ones in open literature and it is shown that the technique introduced here is robust, efficient and easy to implement.