the approximate solutions of fractional differentialequations with antagana-baleanu fractional operator

This article presents the iterative method with the natural variational iteration technique (nvim) to obtain an approximate and numerical solution to the fractional differential equations involving the fractional derivative of atangana-baleaneau in the caputo sense. the algorithm of this method has been analyzed, then the method was applied to two nonlinear fractional differential equations and a linear system. in addition, tables of values and graphs of approximate and accurate solutions were presented. in the end, this method was effective for solving these fractional equations.