JUNG, IL HYO/0000-0002-6086-5124 WOS: 000482145300001 This article studies the dynamical behavior of the analytical solutions of the system of fraction order model of HIV-1 infection. For this purpose, first, the proposed integer order model is converted into fractional order model. Then, Laplace-Adomian decomposition method (L-ADM) is applied to solve this fractional order HIV model. Moreover, the convergence of this method is also discussed. It can be observed from the numerical solution that (L-ADM) is very simple and accurate to solve fraction order HIV model. Department of Mathematics, Pusan National University, South Korea; Higher Education Commission (HEC) of PakistanHigher Education Commission of Pakistan [21-1657/SRGP/RD/HEC/2017] The authors ensure the originality of this research. Upon acceptance, the authors will provide all source files to the journal. This research work has been financially supported by the Department of Mathematics, Pusan National University, South Korea, and the Higher Education Commission (HEC) of Pakistan under grant number 21-1657/SRGP/R&D/HEC/2017.