Mittag-Leffler Euler ∇-differences for Caputo fractional-order systems
Mittag-Leffler Euler ∇-differences for Caputo fractional-order systems
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DOI：
10.1016/j.rinp.2022.105482
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发表时间：
2022-04
影响因子：
5.3
通讯作者：
Tianwei Zhang;Yongkun Li;Jianwen Zhou
中科院分区：
文献类型：
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作者：
Tianwei Zhang;Yongkun Li;Jianwen Zhou
指数型欧拉差分在整数阶微分方程中得到了迅速的发展。但是，很少有文章关注这种差异的分数阶微分方程。利用分数阶微积分中的常数变分方法建立了求解分数阶微分方程的Mittag-Leffler隐式Euler格式的基本结构。更为关键的是，由于得到的差分形式属于隐式Euler差分的范围，因此提出了分数阶PECE算法，在数值计算中有效地解决了这些隐式差分。此外，提出了一种新的非局部差分算子，并给出了相关性质。最后，研究了一类具有短期记忆的非局部差分系统的全局指数稳定解的存在性和有界性。通过算例和数值模拟说明了本文的主要研究结果。
Exponential Euler differences have got rapid development recently for integer-order differential equations. But there are few papers focusing on this difference to fractional differential equations. This paper establishes the basic structure of Mittag-Leffler implicit Euler scheme for fractional differential equations by using the constant variation methods in fractional calculus. More critically, since the acquired difference forms belong to the scope of implicit Euler differences and then the fractional PECE algorithms are proposed to solve these implicit differences in numerical calculations effectively. Besides, a novel nonlocal difference operator is proposed and some relative properties are presented. In the end, the existence and boundedness of a unique globally exponentially stable solution of some nonlocal difference system with short-term memory are investigated. Some calculative examples and numerical simulations are given to illustrate the primary research findings.