Said R. GraceRavi P. AgarwalBillûr KaymakçalanWichuta Sae-jieCairo University, Faculty of EngineeringFlorida Institute of TechnologyGeorgia Southern UniversityMahidol University2018-09-132018-09-132009-07-01Mathematical and Computer Modelling. Vol.50, No.1-2 (2009), 273-286089571772-s2.0-67349216027https://repository.li.mahidol.ac.th/handle/20.500.14594/27497We establish some new oscillation criteria for solutions to the second order nonlinear dynamic equation (a (xΔ)α)Δ (t) + q (t) xβ (t) = 0 on an arbitrary time scale T, where α and β are ratios of positive odd integers, a and q are positive rd-continuous functions on T. The results are obtained when ∫∞ a- 1 / α (s) Δ s < ∞ or ∫∞ a- 1 / α (s) Δ s = ∞. These criteria unify and extend known results for the corresponding half-linear and nonlinear differential and difference equations. Some of our results are new even in the continuous and discrete cases. © 2009 Elsevier Ltd. All rights reserved.Mahidol UniversityComputer ScienceMathematicsArticleSCOPUS10.1016/j.mcm.2008.12.007