Generalized Mittag-Leffler Input Stability of the Fractional Differential Equations
Generalized Mittag-Leffler Input Stability of the Fractional Differential Equations
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DOI：
10.3390/sym11050608
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发表时间：
2019-05-01
期刊：
影响因子：
2.7
通讯作者：
Srivastava, Gautam
中科院分区：
文献类型：
--
作者：
Sene, Ndolane;Srivastava, Gautam
由分数阶导数算子描述的分数阶微分方程的解析解的行为是许多稳定性问题的主要问题。在本文中，我们提出了具有外生输入的分数阶微分方程的新稳定性概念。受 Mittag-Leffler 函数在科学和工程许多领域的成功应用的激励，我们在此介绍我们的工作。 Mittag-Leffler 函数在物理和应用科学某些领域的应用也很常见。在过去的二十年中，此类函数在瑞典数学家 Mittag-Leffler 发现约九年后，由于其在解决物理、生物、工程和地球科学等问题方面的巨大应用潜力而变得引人注目。此外，我们提出了广义的 Mittag-Leffler 输入稳定性条件。左广义分数阶微分方程已被用来帮助创建这个新概念。我们在这里深入研究带有输入的分数阶微分方程的广义 Mittag-Leffler 输入稳定性的 Lyapunov 表征。
The behavior of the analytical solutions of the fractional differential equation described by the fractional order derivative operators is the main subject in many stability problems. In this paper, we present a new stability notion of the fractional differential equations with exogenous input. Motivated by the success of the applications of the Mittag-Leffler functions in many areas of science and engineering, we present our work here. Applications of Mittag-Leffler functions in certain areas of physical and applied sciences are also very common. During the last two decades, this class of functions has come into prominence after about nine decades of its discovery by a Swedish Mathematician Mittag-Leffler, due to the vast potential of its applications in solving the problems of physical, biological, engineering, and earth sciences, to name just a few. Moreover, we propose the generalized Mittag-Leffler input stability conditions. The left generalized fractional differential equation has been used to help create this new notion. We investigate in depth here the Lyapunov characterizations of the generalized Mittag-Leffler input stability of the fractional differential equation with input.