Discrete Dynamics in Nature and Society
Volume 2012 (2012), Article ID 157301, 22 pages
Research Article

Some Opial Dynamic Inequalities Involving Higher Order Derivatives on Time Scales

Department of Mathematics, Faculty of Science, Mansoura University, Mansoura 35516, Egypt

Received 25 April 2012; Accepted 16 August 2012

Academic Editor: Eric R. Kaufmann

Copyright © 2012 Samir H. Saker. 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.


We will prove some new Opial dynamic inequalities involving higher order derivatives on time scales. The results will be proved by making use of Hölder's inequality, a simple consequence of Keller's chain rule and Taylor monomials on time scales. Some continuous and discrete inequalities will be derived from our results as special cases.