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Discrete Dynamics in Nature and Society
Volume 2017, Article ID 9050289, 15 pages
https://doi.org/10.1155/2017/9050289
Research Article

Analysis of a Class of Fractional Nonlinear Multidelay Differential Systems

1College of Applied Mathematics, Shanxi University of Finance and Economics, Taiyuan, Shanxi 030031, China
2Department of Mathematics, Guizhou University, Guiyang, Guizhou 550025, China
3Department of Mathematics, Xiangtan University, Xiangtan, Hunan 411105, China
4Nonlinear Analysis and Applied Mathematics (NAAM) Research Group, Faculty of Science, King Abdulaziz University, Jeddah 21589, Saudi Arabia

Correspondence should be addressed to Yong Zhou; nc.ude.utx@uohzy

Received 31 July 2017; Accepted 30 August 2017; Published 15 October 2017

Academic Editor: Antonio Iannizzotto

Copyright © 2017 Zhuoyan Gao et al. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.

Abstract

We address existence and Ulam-Hyers and Ulam-Hyers-Mittag-Leffler stability of fractional nonlinear multiple time-delays systems with respect to two parameters’ weighted norm, which provides a foundation to study iterative learning control problem for this system. Secondly, we design PID-type learning laws to generate sequences of output trajectories to tracking the desired trajectory. Two numerical examples are used to illustrate the theoretical results.