One of the most important tools used to create a secure environment for transmitting information is the use of chaotic systems. In the present work, chaotic systems have been improved by using differential equations based on fractional calculations. The structure of the improved system is studied by using various tests. And as an application of the new system, a cryptographic algorithm based on proposed system and framelet transmission is introduced and various types of security tests are examined on it.

中文翻译：

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基于分数阶混沌系统和框架变换的图像加密算法

用于创建安全的信息传输环境的最重要工具之一是混沌系统的使用。在目前的工作中，混沌系统已经通过使用基于分数计算的微分方程进行了改进。通过各种试验研究了改进系统的结构。并作为新系统的应用，介绍了一种基于提议系统和框架传输的密码算法，并对其进行了各种类型的安全测试。