Numerical simulation for SI model with variable-order fractional

In this paper numerical studies for the variable-order fractional delay differential equations are presented. Adams-Bashforth-Moulton algorithm has been extended to study this problem, where the derivative is defined in the Caputo variable-order fractional sense. Special attention is given to prove the error estimate of the proposed method. Numerical test examples are presented to demonstrate utility of the method. Chaotic behaviors are observed in variable-order one dimensional delayed systems.