Quadrature rule for Abel’s equations: Uniformly approximating fractional derivatives |
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Authors: | Hiroshi Sugiura Takemitsu Hasegawa |
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Institution: | 1. Department of Information Systems and Mathematical Sciences, Nanzan University, Seto, Aichi, 489-0863, Japan;2. Department of Information Science, University of Fukui, Fukui, 910-8507, Japan |
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Abstract: | An automatic quadrature method is presented for approximating fractional derivative Dqf(x) of a given function f(x), which is defined by an indefinite integral involving f(x). The present method interpolates f(x) in terms of the Chebyshev polynomials in the range 0, 1] to approximate the fractional derivative Dqf(x) uniformly for 0≤x≤1, namely the error is bounded independently of x. Some numerical examples demonstrate the performance of the present automatic method. |
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Keywords: | Abel integral equation Fractional derivative Chebyshev interpolation Quadrature rule Automatic quadrature Error analysis Uniform approximation |
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