论文标题
短记忆分数微分方程的稳定性分析
Stability Analysis of Short Memory Fractional Differential Equations
论文作者
论文摘要
在本文中，定义了具有短期内存特性的分数衍生物，可以将其视为Caputo分数衍生物的扩展。然后，讨论了短存储器分数衍生物的某些属性。此外，还显示了一类短存储器分数系统的比较定理，通过该类别，可以建立短存储器分数系统与CAPUTO分数系统之间的某些关系。通过应用比较定理和Lyapunov直接方法，获得了一些足够的标准，这可以确保某些短记忆分数方程的渐近稳定性。此外，提出了一个特殊的结果，可以直接判断某些特殊系统的稳定性。最后，提供了三个示例以证明主要结果的有效性。
In this paper, a fractional derivative with short-term memory properties is defined, which can be viewed as an extension of Caputo fractional derivative. Then, some properties of the short memory fractional derivative are discussed. Also, a comparison theorem for a class of short memory fractional systems is shown, via which some relationship between short memory fractional systems and Caputo fractional systems can be established. By applying the comparison theorem and Lyapunov direct method, some sufficient criteria are obtained, which can ensure the asymptotic stability of some short memory fractional equations. Moreover, a special result is presented, by which the stability of some special systems can be judged directly. Finally, three examples are provided to demonstrate the effectiveness of the main results.
