A Convergent Algorithm for Solving Higher-Order Nonlinear Fractional Boundary Value Problems

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40 Citations (Scopus)

Abstract

We present a numerical algorithm for solving nonlinear fractional boundary value problems of order n, n ∈ IN. The Bernstein polynomials (BPs) are redefined in a fractional form over an arbitrary interval [a, b]. Theoretical results related to the ractional Bernstein polynomials (FBPs) are proven. The well-known shooting technique is extended for the numerical treatment of nonlinear fractional boundary value problems of arbitrary order. The initial value problems were solved using a collocation method with collocation points at the location of the local maximum of the FBPs. Several examples are discussed to illustrate the efficiency and accuracy of the present scheme.

Original languageEnglish
Pages (from-to)1423-1440
Number of pages18
JournalFractional Calculus and Applied Analysis
Volume18
Issue number6
DOIs
Publication statusPublished - Dec 1 2015

Keywords

  • Caputo's fractional derivative
  • Fractional Bernstein polynomials
  • collocation method
  • shooting method

ASJC Scopus subject areas

  • Analysis
  • Applied Mathematics

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