Abstract
The aim of this paper is to analyze the chaotic dynamics of a novel 2D fractional order discrete Ushiki map using Caputo-like delta fractional difference operator. The dynamical nature of the proposed discrete fractional Ushiki map is examined with evolution of time states and bifurcation diagrams. In addition, control law aimed at stabilizing the proposed map and the synchronization of the discrete fractional order Ushiki map are also presented. Numerical examples are exhibited to demonstrate the validity of the theoretical findings of the study.