Approximation of fractional integrals by means of derivatives

• Author(s): Pooseh, S. ; Almeida, R. ; Torres, D. F. M.
• Date: 2012
• Persistent ID: http://hdl.handle.net/10773/11652
• Origin: RIA - Repositório Institucional da Universidade de Aveiro
• Subject(s): Fractional integrals; Numerical approximation; Error estimation
• Document Type: Article
• Language: English

Description

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 is an element of 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.