Caputo-Hadamard fractional chaotic maps

In this paper, we proposed a new fractional two dimensional trigonometric combined discrete chaotic mapping (2D-TCDCM) and a fractional 2-D Kawakami map within Caputo-Hadamard fractional difference. We observed the dynamic behaviours of the proposed Caputo-Hadamard fractional maps, including fractal graph, maximum lyapunov exponent, phase trajectory and randomness test. We illustrate the advantage of using Caputo-Hadamard fractional difference. As a conclusion, we get the condition of the proposed fractional map to behave chaotically with physics background.