Abstract
This manuscript is devoted to establish the existence theory of solutions to HIV - 1 infection model of CD4+ T-cells with fractional order derivative. The corresponding fractional order derivative is considered in CaputoFabrizio sense, which possesses more important characteristics in mathematical modeling. With the help of Sumudu transform and Picard successive approximation techniques, some interesting results are obtained. Existence and uniqueness for the equilibrium solutions are discussed. Some numerical simulations are provided to show the effectiveness of the theoretical results.