Positive solutions of an abstract fractional semipositone differential system model for bioprocesses of HIV infection

• The abstract fractional dynamics model is based on a class of bioprocesses of HIV infection.
• The nonlinear terms and boundary conditions all depend on fractional derivatives of unknown functions.
• The system is singular and semipositone.
• The system involves some uncertain parametrical variations λλ.

Fractional order derivative is nonlocal which exhibits a long time memory behavior. With advantage of these, fractional order dynamic system models are more accurate than integer order ones in understanding the dynamic behavior of bioprocesses such as HIV infection. In this paper, we systematically study the existence of positive solutions of an abstract fractional semipositone differential system involving integral boundary conditions arising from the study of HIV infection models. By using the fixed point theorem in cone, some new results are established and an example is given to demonstrate the application of our main results.