✦ LIBER ✦
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
No coin nor oath required. For personal study only.
✦ 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.