A Collocation Method for the Numerical Solution of Nonlinear Fractional Dynamical Systems

Abstract

Fractional differential problems are widely used in applied sciences. For this reason, there is a great interest in the construction of efficient numerical methods to approximate their solution. The aim of this paper is to describe in detail a collocation method suitable to approximate the solution of dynamical systems with time derivative of fractional order. We will highlight all the steps necessary to implement the corresponding algorithm and we will use it to solve some test problems. Two Mathematica Notebooks that can be used to solve these test problems are provided.

Keywords

• fractional differential equation
• nonlinear dynamical system
• B-spline
• collocation method