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
arXiv:1912.11919 · doi:10.1007/s00500-019-04645-5
Abstract
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.
arXiv commentThis is a post-peer-review, pre-copyedit version of an article published in Soft Computing. The final authenticated version is available online at [http://dx.doi.org/10.1007/s00500-019-04645-5]. Paper Submitted 26-April-2019; Revised 02-Nov-2019; Accepted 17-Dec-2019
References in corpus (4)
- The Variable-Order Fractional Calculus of Variations
- Optimal control of a fractional order epidemic model with application to human respiratory syncytial virus infection
- A numerical approach for solving fractional optimal control problems using modified hat functions
- A space-time pseudospectral discretization method for solving diffusion optimal control problems with two-sided fractional derivatives