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The paper aims to investigate an HIV epidemic fractional model. The fractional derivatives are described in the sense of Caputo operator and Constant Proportional Caputo (CPC) operator, respectively. The existence of solution and stability analysis of the HIV mathematical model have been presented for the CPC fractional operator. The model is attempted to solve by using the fractional differential transform method and the Laplace Adomian decomposition method, respectively. The methods are further examined for different values of fractional order α. The findings show that the methods are effective for providing better results.