An expansion formula with higher-order derivatives for fractional operators of variable order
Classical Analysis and ODEs
2013-10-29 v1 Numerical Analysis
Optimization and Control
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.
Keywords
Cite
@article{arxiv.1309.4899,
title = {An expansion formula with higher-order derivatives for fractional operators of variable order},
author = {Ricardo Almeida and Delfim F. M. Torres},
journal= {arXiv preprint arXiv:1309.4899},
year = {2013}
}
Comments
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