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The main determination of this task is to investigate a mathematical system numerically and figure out the possible dynamics of transmission of HIV/AIDS disease in existence of an aware community. In our work, we consider a mathematical system of HIV/AIDS transmission in existence of awareness effect and the model is considered with three different singular and non-singular fractional operators. Further, the existence results of the arbitrary-order model is interrogated through Picard-Lindelof approach. We show some numerical algorithms for achieving an approximate solution of the suggested model such as a predictor–corrector numerical scheme for Caputo derivative, two-step Adams-Bashforth numerical technique for CF derivative and Adams-type predictor–corrector numerical technique for AB derivative. The numerical simulations of the obtained numerical results for the suggested system are suggested for distinct values of arbitrary order.