A continuous time Bertrand duopoly game with fractional delay and conformable derivative: Modeling, discretization process, Hopf bifurcation, and chaos

Abstract

The purpose of this paper is three-fold. First, we present a discretization process to obtain numerical solutions of a conformable fractional-order system with delays. Second, we extend the classical Bertrand duopoly game with integer delays to that with fractional delays. Third, we extend the game based on ordinary differential derivative to that based on conformable fractional-order derivative. Finally, we analyze the local stability, Hopf bifurcation, and chaos of the proposed game model.