On analysis of fractional order HIV infection model with the adaptive immune response under Caputo operator

The present work investigates the fractional dynamics of a system concerned with the human immuno-deficiency virus (HIV) disease with cytotoxic T-lymphocyte (CTL), anti-bodies and two saturated rates. The system is characterized by five non-linear compartments which examine the conditions of un-infected cells, infected cells, cells without HIV, CTL immune responses, and antibodies. This problem aims to examine the existence and uniqueness of some well-known theory of fixed point. More precisely, Ulam Hyer’s stability was used to analyze the system’s stability. The approximate solution is carried out using fractional Adams Bash-forth method techniques. Using MATLAB, some numerical simulations are carried out by the obtained scheme at different non-integer order along with the comparison of integer order.