Affiliation:
1. Department of Mathematical Sciences College of Science, P. O. Box 15551, UAE University Al-Ain, UNITED ARAB EMIRATES
Abstract
Abstract
We present a numerical algorithm for solving nonlinear fractional boundary value problems of order n, n ∈ ℕ. 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.
Subject
Applied Mathematics,Analysis
Cited by
46 articles.
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