An expansion formula with higher-order derivatives for fractional operators of ...

• Author(s): Almeida, R. ; Torres, D.F.M.
• Date: 2013
• Persistent ID: http://hdl.handle.net/10773/11891
• Origin: RIA - Repositório Institucional da Universidade de Aveiro
• Subject(s): analytical error; marchaud fractional order; mathematical analysis; mathematical parameters; riemann liouville fractional order
• Document Type: Article
• Language: English

Description

We obtain approximation formulas for fractional integrals and derivatives of Riemann-Liouville and Marchaud types with a variable fractional order. The approximations involve integer-order derivatives only. An estimation for the error is given. The efficiency of the approximation method is illustrated with examples. As applications, we show how the obtained results are useful to solve differential equations, and problems of the calculus of variations that depend on fractional derivatives of Marchaud type.