Affiliations: [a] Oxbridge College, Kunming University of Science and Technology, Kunming, China
| [b] City College, Kunming University of Science and Technology, Kunming, China
Correspondence:
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Corresponding author. Tianwei Zhang, City College, Kunming University of Science and Technology, Kunming 650051, China. E-mail: zhang@kust.edu.cn.
Abstract: Exponential Euler differences for semi-linear differential equations of first order have got rapid development in the past few years and a variety of exponential Euler difference methods have become very significant researching topics. In allusion to fuzzy genetic regulatory networks of fractional order, this paper firstly establishes a novel difference method called Mittag-Leffler Euler difference, which includes the exponential Euler difference. In the second place, the existence of a unique global bounded solution and equilibrium point, global exponential stability and synchronization of the derived difference models are investigated. Compared with the classical fractional Euler differences, fuzzy Mittag-Leffler discrete-time genetic regulatory networks can better depict and retain the dynamic characteristics of the corresponding continuous-time models. What’s more important is that it starts a new avenue for studying discrete-time fractional-order systems and a set of theories and methods is constructed in studying Mittag-Leffler discrete models.
