To improve the chaos complexity of existing chaotic maps, the fractional difference form of sine chaotification model (FSCM) is proposed in this paper based on discrete fractional calculus. In order to show its effect, we apply it to three chaotic maps. And the bifurcation diagrams and Lyapunov exponent of the generated new map are studied numerically. The experimental results show that FSCM has more stable and efficient performance. In addition, the dynamic behavior of the generated new map varies with the fractional order, which can be observed through analysis. Finally, FSCM is used for image encryption to show its performance in practical applications. The analysis of the results shows that the chaotic behavior of the fractional map generated by FSCM is more complex and its encryption effect is better.

为了提高现有混沌图的混沌复杂度，提出了基于离散分数阶微积分的正弦混沌模型分数差分形式。为了显示其效果，我们将其应用于三个混沌图。并对生成的新图的分叉图和李雅普诺夫指数进行了数值研究。实验结果表明，FSCM具有更稳定，更高效的性能。此外，生成的新图的动态行为会随分数阶而变化，这可以通过分析来观察。最后，FSCM用于图像加密以显示其在实际应用中的性能。结果分析表明，FSCM生成的分数图的混沌行为更为复杂，加密效果更好。