An Expansion Formula with Higher-Order Derivatives for Fractional Operators of Variable Order. (10th November 2013)

• Record Type: Journal Article
• Authors: Almeida, Ricardo; Torres, Delfim F. M.
• Other Names: Atangana A. Academic Editor.; Noutchie S. C. O. Academic Editor.; Secer A. Academic Editor.
• Is Part Of: TheScientificWorldjournal. Volume 2013(2013)
• Publication Date: 2013-11-10
• Subjects: Science -- Periodicals; Technology -- Periodicals; Medicine -- Periodicals; 505
• DOI: 10.1155/2013/915437
• Languages: English
• ISSNs: 2356-6140

Abstract

Abstract : 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.