Approximation of fractional integrals by means of derivatives

Details Approximation of fractional integrals by means of derivatives Approximation of fractional integrals by means of derivatives

2012-01-25

arxiv.org/abs/1201.5224v1

Mathematics

Classical Analysis and ODEs

Submitted 15-10-2011; revised 24-01-2012; accepted 25-01-2012; for publication in Computers and Mathematics with Applications

Scientific paper

10.1016/j.camwa.2012.01.068

We obtain a new decomposition of the Riemann-Liouville operators of fractional integration as a series involving derivatives (of integer order). The new formulas are valid for functions of class $C^n$, $n \in \mathbb{N}$, and allow us to develop suitable numerical approximations with known estimations for the error. The usefulness of the obtained results, in solving fractional integral equations and fractional problems of the calculus of variations, is illustrated.

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