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Approximation of fractional integrals by means of derivatives

Abstract : 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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Submitted on : Wednesday, August 22, 2012 - 2:17:42 PM
Last modification on : Tuesday, June 1, 2021 - 9:50:04 PM

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Shakoor Pooseh, Ricardo Almeida, Delfim F. M. Torres. Approximation of fractional integrals by means of derivatives. Computers & Mathematics with Applications, Elsevier, 2012, ⟨10.1016/j.camwa.2012.01.068⟩. ⟨hal-00724720⟩



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