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Citation - WoS: 4
New Criteria on Oscillatory and Asymptotic Behavior of Third-Order Nonlinear Dynamic Equations With Nonlinear Neutral Terms
(Mdpi, 2021) Grace, Said R.; Alzabut, Jehad; Ozbekler, Abdullah
In the paper, we provide sufficient conditions for the oscillatory and asymptotic behavior of a new type of third-order nonlinear dynamic equations with mixed nonlinear neutral terms. Our theorems not only improve and extend existing theorems in the literature but also provide a new approach as far as the nonlinear neutral terms are concerned. The main results are illustrated by some particular examples.
Citation - WoS: 10
Citation - Scopus: 14
On the Oscillation of Non-Linear Fractional Difference Equations With Damping
(Mdpi, 2019) Alzabut, Jehad; Muthulakshmi, Velu; Ozbekler, Abdullah; Adigilzel, Hakan
In studying the Riccati transformation technique, some mathematical inequalities and comparison results, we establish new oscillation criteria for a non-linear fractional difference equation with damping term. Preliminary details including notations, definitions and essential lemmas on discrete fractional calculus are furnished before proceeding to the main results. The consistency of the proposed results is demonstrated by presenting some numerical examples. We end the paper with a concluding remark.