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.
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The Scientific World Journal, Hindawi Publishing Corporation, 2013, 2013, 11p. 〈10.1155/2013/915437〉
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Soumis le : lundi 22 septembre 2014 - 17:14:56
Dernière modification le : mercredi 27 juillet 2016 - 14:48:48

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Ricardo Almeida, Delfim F. M. Torres. An expansion formula with higher-order derivatives for fractional operators of variable order. The Scientific World Journal, Hindawi Publishing Corporation, 2013, 2013, 11p. 〈10.1155/2013/915437〉. 〈hal-01066990〉

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