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Discrete Dynamics in Nature and Society
Volume 2016 (2016), Article ID 6847956, 9 pages
http://dx.doi.org/10.1155/2016/6847956
Research Article

Comparison Criteria for Nonlinear Functional Dynamic Equations of Higher Order

1Department of Mathematics, Faculty of Science, University of Hail, Hail 2440, Saudi Arabia
2Department of Mathematics, Faculty of Science, Mansoura University, Mansoura 35516, Egypt
3Department of Engineering Mathematics, Faculty of Engineering, Cairo University, Orman, Giza 12221, Egypt

Received 9 February 2016; Accepted 22 May 2016

Academic Editor: Yuriy V. Rogovchenko

Copyright © 2016 Taher S. Hassan and Said R. Grace. 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 will consider the higher order functional dynamic equations with mixed nonlinearities of the form , on an above-unbounded time scale , where , ,   with  , and . The function is a rd-continuous function such that for . The results extend and improve some known results in the literature on higher order nonlinear dynamic equations.