KAOUTHER BOUCHAMA2022-03-032022-03-032022http://dspace.univ-msila.dz:8080//xmlui/handle/123456789/28103The main objective of this thesis is to present the finite difference method to approximate fractional derivatives, in order to find numerical solutions to linear fractional differentials equations and partial differentials equations, involving Caputo-Hadamard and Caputo-Katugampola fractional derivative. As such, the convergence and stability of the numerical schemes are proved using mathematical induction. illustrative examples have been presented to show the effectiveness and validity of our methodFractional differential equations, Finite difference methods, Caputo-Hadamard fractional derivative, Caputo-Katugampola derivative, Convergence, StabilityThesis