Dérivée d'ordre fractionnaire de Grunwald-Letnikov

Abstract

The work presented in this memory is part of the framework of adapting with fractional calculus by introducing the fractional integration and fractional di erentiation linear operators of Riemann-Liouville and Gr unwald-Letnikov. Particular attention is devoted to the auxiliary tools necessary to de ne these new concepts as certain special functions (Gamma-b^eta...) and to the Laplace transform technique. Then, we present the de nitions of fractional derivatives in the sens of Riemann- Liouville and Gr unwald-Letnikov. Also, we present some basic properties of di erintegrals, such as linearity, the Leibniz rule and composition. Finally, we explain the links between these derivatives