title: 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.
authors: Center for Research and Development in Mathematics and Applications (CIDMA), Department of Mathematics, University of Aveiro, 3810-193 Aveiro, Portugal.
authors: Ricardo
authors: R
authors: Almeida
authors: Delfim F M
authors: DF
authors: Torres
mesh_terms: D008433:Mathematics; D008962:Models, Theoretical