Journal
FRACTIONAL CALCULUS AND APPLIED ANALYSIS
Volume 18, Issue 6, Pages 1423-1440Publisher
WALTER DE GRUYTER GMBH
DOI: 10.1515/fca-2015-0082
Keywords
fractional Bernstein polynomials; shooting method; collocation method; Caputo's fractional derivative
Funding
- United Arab Emirates University Research Affairs [COS/IRG-16/14]
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We present a numerical algorithm for solving nonlinear fractional boundary value problems of order n, n epsilon IN The Bernstein polynomials (BPs) are redefined in a fractional form over an arbitrary interval [a, b]. Theoretical results related to the fractional 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.
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