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Advances in Mathematical Physics
Volume 2017 (2017), Article ID 6971743, 6 pages
https://doi.org/10.1155/2017/6971743
Research Article

The Asymptotic Behaviours of a Class of Neutral Delay Fractional-Order Pantograph Differential Equations

School of Mathematics and Statistics, Xuchang University, Xuchang 461000, China

Correspondence should be addressed to Baojun Miao; moc.621@5002oaimjb

Received 1 April 2017; Revised 8 July 2017; Accepted 3 August 2017; Published 22 October 2017

Academic Editor: Antonio Scarfone

Copyright © 2017 Baojun Miao and Xuechen Li. 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

By using fractional calculus and the summation by parts formula in this paper, the asymptotic behaviours of solutions of nonlinear neutral fractional delay pantograph equations with continuous arguments are investigated. The asymptotic estimates of solutions for the equation are obtained, which may imply asymptotic stability of solutions. In the end, a particular case is provided to illustrate the main result and the speed of the convergence of the obtained solutions.