Journal Paper

In this article, we develop a simple mathematical GNU Octave/MATLAB code that is
easy to modify for the simulation of mathematical models governed by fractional-order differential
equations, and for the resolution of fractional-order optimal control problems through Pontryagin’s
maximum principle (indirect approach to optimal control). For this purpose, a fractional-order model
for the respiratory syncytial virus (RSV) infection is considered. The model is an improvement
of one first proposed by the authors in 2018. The initial value problem associated with the RSV
infection fractional model is numerically solved using Garrapa’s fde12 solver and two simple
methods coded here in Octave/MATLAB: the fractional forward Euler’s method and the predictevaluate-
correct-evaluate (PECE) method of Adams–Bashforth–Moulton. A fractional optimal control
problem is then formulated having treatment as the control. The fractional Pontryagin maximum
principle is used to characterize the fractional optimal control and the extremals of the problem are
determined numerically through the implementation of the forward-backward PECE method. The
implemented algorithms are available on GitHub and, at the end of the paper, in appendixes, both
for the uncontrolled initial value problem as well as for the fractional optimal control problem, using
the free GNU Octave computing software and assuring compatibility with MATLAB.