Lyapunov functions for fractional-order systems in biology: methods and applications
Abstract
We prove new estimates of the Caputo derivative of order for some specific functions. The estimations are shown useful to construct Lyapunov functions for systems of fractional differential equations in biology, based on those known for ordinary differential equations, and therefore useful to determine the global stability of the equilibrium points for fractional systems. To illustrate the usefulness of our theoretical results, a fractional HIV population model and a fractional cellular model are studied. More precisely, we construct suitable Lyapunov functionals to demonstrate the global stability of the free and endemic equilibriums, for both fractional models, and we also perform some numerical simulations that confirm our choices.
Keywords
Cite
@article{arxiv.2008.09177,
title = {Lyapunov functions for fractional-order systems in biology: methods and applications},
author = {Adnane Boukhouima and Khalid Hattaf and El Mehdi Lotfi and Marouane Mahrouf and Delfim F. M. Torres and Noura Yousfi},
journal= {arXiv preprint arXiv:2008.09177},
year = {2020}
}
Comments
This is a preprint of a paper whose final and definite form is published in 'Chaos, Solitons & Fractals', available at [http://dx.doi.org/10.1016/j.chaos.2020.110224]. Submitted 25-May-2020; Revised 25-July-2020; Accepted 19-August-2020