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

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.

This is a preprint of a paper whose final and definite form will be published in The Scientific World Journal (http://www.hindawi.com/journals/tswj). Submitted 27-Aug-2013; accepted 19-Sept-2013

References in corpus (3)

• Numerical Approximations of Fractional Derivatives with Applications
• Variable Order Fractional Variational Calculus for Double Integrals
• A Generalized Fractional Calculus of Variations

Cited by in corpus (1)

• Optimality Conditions for Fractional Variational Problems with Dependence on a Combined Caputo Derivative of Variable Order