Numerical solution of some fractional dynamical systems in medicine involving non-singular kernel with vector order

Abstract

In this paper, we propose systems of variable-order fractional equations for some problems in medicine. These problems include the dynamics of Zika virus fever and HIV infection of CD4$^+$ T-cells. Two types of non-local fractional derivatives are considered and compared in these dynamics: The Liouville-Caputo's definition and a definition involving non-singular Mittag-Leffler kernel. Predictor-corrector methods are described for simulating the corresponding dynamical systems.