A study of fractional HIV-1 infection of CD4+ T–cells of
immunodeficiency syndrome with the effect of antiviral drug therapy
through non-singular derivative
Abstract
In this research paper, the HIV-1 infection of CD4+ T-cells fractional
mathematical model with the effect of antiviral drug therapy is handled
by applying three new computational schemes to this biological model to
investigate its analytical explicit wave solutions. This mathematical
model is used to predict the evolution of the population dynamical
systems involving virus particles. The modified Khater method, the
extended simplest equation method, and sech–tanh method with a new
fractional operator (Atangana–Baleanu derivative operator) is employing
to find the analytical solutions in various distinct new formulas of the
biological suggested model. Moreover, the stability of the obtained
solutions is investigated by using the characterizes of the Hamiltonian
system to show their applicability in making the antivirals that protect
our human life. Some plots are explained under specific conditions of
the contained constants to reveal the dynamical behavior of the
evolution of the population dynamical systems involving virus particles.
A comparison between our results and that obtained in previous work is
also represented and discussed in detail to show the novelty for our
solutions. The performance of the used methods shows power, practical,
and ability to apply to other nonlinear partial differential equations.