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Quadrature rule for Abel’s equations: Uniformly approximating fractional derivatives

✍ Scribed by Hiroshi Sugiura; Takemitsu Hasegawa


Publisher
Elsevier Science
Year
2009
Tongue
English
Weight
514 KB
Volume
223
Category
Article
ISSN
0377-0427

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✦ Synopsis


An automatic quadrature method is presented for approximating fractional derivative D q f (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 D q f (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.