Abstract
In this manuscript, we investigate existence theory as well as stability results to the biological model of HIV (human immunodeficiency virus) disease. We consider the proposed model under Caputo-Fabrizio derivative (CFD) with exponential kernel. We investigate the suggested model from other perspectives by using fixed point approached derive its existence and uniqueness of solution. Further the stability of the concerned solution in Hyers-Ulam sense is also investigated. Further to derive the approximate solution in the form of series to the considered model, we use integral transform of Laplace coupled with Adomian decomposition method. The concerned technique is powerful tool to find semi-analytical solutions to many nonlinear problems. Finally, we demonstrate the results of approximate solutions through graphs by using Matlab.