Abstract
In this work, new conditions were obtained for the oscillation of solutions of fourth-order non-linear neutral differential equations (NDEs) using the Riccati technique. These oscillation criteria complement and improve those of Chatzarakis et al. (2019). Symmetry plays an important role in determining the right way to study these equation. An example is given to illustrate our theory.
Highlights
Neutral differential equations (NDEs) are differential equations with delays, where the delays can appear in both the state variables and their time derivatives
Properties of delay differential equations were used in the study of singular fractional order differential equations [7,8], and other types of fractional operators such as the fractional nabla applied to difference equations where the memory effect appears [9,10]
Using these Lemmas and the Riccati transform, we prove the oscillation of Equation (1), and provide an example
Summary
Neutral differential equations (NDEs) are differential equations with delays, where the delays can appear in both the state variables and their time derivatives. For results of fourth-order non-linear neutral differential equations, we recommend [32,33,34,35,36,37,38,39,40,41] and their references therein. We consider the following class of fourth-order non-linear NDE: L0x + q (y) x α (π (y)) = 0, y ≥ y0 ,. Using these Lemmas and the Riccati transform, we prove the oscillation of Equation (1), and provide an example.
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