Quadrature rule for Abel's equations : uniformly approximating fractional derivatives uniformly approximating fractional derivatives (High Performance Algorithms for Computational Science and Their Applications)

An automatic quadrature method is presented for approximating fractional derivative D^qf(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^qf(x) uniformly for [email protected][email protected]?1, namely the error is bounded independently of x. Some numerical examples demonstrate the performance of the present automatic method.

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