YAHIAOUI YOUCEFI, AsyaMEKHALF, Kheira2024-12-112024-12-112023http://dspace.univ-temouchent.edu.dz/handle/123456789/5892The 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 derivativesfrThesis