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

Year 2019, Volume: 2 Issue: 4, 160 - 168, 25.12.2019

Babak Shiri , Dumitru Baleanu

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.

Keywords

Dynamical systems, Zika virus fever, HIV infection of CD4$^+$ T-cells, Predictor-corrector methods, System of variable order fractional equations

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