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 nonlocal 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. © 2019, Cankaya University. All rights reserved.