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Fractional variational iteration method FVIM is performed to give an approximate analytical solution of nonlinear fractional Riccati differential equation. Fractional derivatives are described in the Riemann-Liouville derivative. A new application of fractional variational iteration method FVIM was extended to derive analytical solutions in the form of a series for these equations. The behavior of the solutions and the effects of different values of fractional order α are indicated graphically. The results obtained by the FVIM reveal that the method is very reliable, convenient, and effective method for nonlinear differential equations with modified Riemann-Liouville derivative

Abstract-In this article, homotopy perturbation method is implemented to give approximate and analytical solutions of nonlinear ordinary differential equation systems such as human Tcell lymphotropic virus I (HTLV-I) infection of CD4+ T-cells model. The proposed scheme is based on homotopy perturbation method (HPM), Laplace transform and Padé approximants. The results to get the homotopy perturbation method (HPM) is applied Padé approximants. Our proposed approach showed results to analytical solutions of nonlinear ordinary differential equation systems. Some plots are presented to show the reliability and simplicity of the methods.