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We propose a new spectral method, based on two classes of hat functions, forsolving systems of fractional differential equations. The fractional derivativeis considered in the Caputo sense. Properties of the basis functions, Caputoderivatives, and Riemann-Liouville fractional integrals, are used to reduce themain problem to a system of nonlinear algebraic equations. By analyzing indetail the resulting system, we show that the method needs few computationalefforts. Two test problems are considered to illustrate the efficiency andaccuracy of the proposed method. Finally, an application to a recentmathematical model in epidemiology is given, precisely to a system offractional differential equations modeling the respiratory syncytial virusinfection.

soft computing

A new spectral method based on two classes of hat functions for solving  systems of fractional differential equations and an application to  respiratory syncytial virus infection