Numerical solutions of fractional differential equations by using fractional explicit Adams method

Nur Amirah Zabidi, Zanariah Abdul Majid, Adem Kilicman, Faranak Rabiei

Research output: Contribution to journalArticleResearchpeer-review

15 Citations (Scopus)

Abstract

Differential equations of fractional order are believed to be more challenging to compute compared to the integer-order differential equations due to its arbitrary properties. This study proposes a multistep method to solve fractional differential equations. The method is derived based on the concept of a third-order Adam–Bashforth numerical scheme by implementing Lagrange interpolation for fractional case, where the fractional derivatives are defined in the Caputo sense. Furthermore, the study includes a discussion on stability and convergence analysis of the method. Several numerical examples are also provided in order to validate the reliability and efficiency of the proposed method. The examples in this study cover solving linear and nonlinear fractional differential equations for the case of both single order as α ∈ (0, 1) and higher order, α ∈ [1, 2), where α denotes the order of fractional derivatives of Dα y(t). The comparison in terms of accuracy between the proposed method and other existing methods demonstrate that the proposed method gives competitive performance as the existing methods.

Original languageEnglish
Article number1675
Number of pages23
JournalMathematics
Volume8
Issue number10
DOIs
Publication statusPublished - Oct 2020

Keywords

  • Fractional differential equation
  • Fractional Riccati differential equation
  • Higher order FDE
  • Linear FDE
  • Multistep method
  • Nonlinear FDE
  • Single order FDE

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