  We propose a new spectral method, based on two classes of hat functions, for
solving systems of fractional differential equations. The fractional derivative
is considered in the Caputo sense. Properties of the basis functions, Caputo
derivatives, and Riemann-Liouville fractional integrals, are used to reduce the
main problem to a system of nonlinear algebraic equations. By analyzing in
detail the resulting system, we show that the method needs few computational
efforts. Two test problems are considered to illustrate the efficiency and
accuracy of the proposed method. Finally, an application to a recent
mathematical model in epidemiology is given, precisely to a system of
fractional differential equations modeling the respiratory syncytial virus
infection.
