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

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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.

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Authors and Affiliations

  1. Department of Mathematical Sciences College of Science, UAE University Al-Ain, P. O. Box 15551, United Arab Emirates

    Qasem M. Al-Mdallal & Mohamed A. Hajji

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  1. Qasem M. Al-Mdallal
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  2. Mohamed A. Hajji
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Correspondence to Qasem M. Al-Mdallal.

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Al-Mdallal, Q.M., Hajji, M.A. A Convergent Algorithm for Solving Higher-Order Nonlinear Fractional Boundary Value Problems. FCAA 18, 1423–1440 (2015). https://doi.org/10.1515/fca-2015-0082

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