Second-Order Non-Canonical Neutral Differential Equations with Mixed Type: Oscillatory Behavior

Moaaz, Osama; Nabih, Amany; Alotaibi, Hammad; Hamed, Y. S.

doi:10.3390/sym13020318

Cited by 2 publications

(2 citation statements)

References 19 publications

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“…During the past few years, there has been a constant interest in obtaining sufficient conditions for oscillatory and non-oscillatory properties of different order differential equations. For some groups that developed equations of the second order see [1][2][3][4], for the fourth order see [5][6][7][8] and for higher-order we refer the reader to [9][10][11][12].…”

Section: Notationmentioning

confidence: 99%

An Improved Approach to Investigate the Oscillatory Properties of Third-Order Neutral Differential Equations

Moaaz

Alnafisah

2023

Mathematics

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In this work, by considering a third-order differential equation with delay-neutral arguments, we investigate the oscillatory behavior of solutions. It is known that the relationships between the solution and its derivatives of different orders, as well as between the solution and its corresponding function, can help to obtain more efficient oscillation criteria for differential equations of neutral type. So, we deduce some new relationships of an iterative nature. Then, we test the effect of these relationships on the criteria that exclude positive solutions to the studied equation. By comparing our results with previous results in the literature, we show the importance and novelty of the new results.

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Section: Notationmentioning

confidence: 99%

An Improved Approach to Investigate the Oscillatory Properties of Third-Order Neutral Differential Equations

Moaaz

Alnafisah

2023

Mathematics

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“…The study of oscillation for ordinary and fractional DE solutions with delay, neutral, mixed, or damping terms is currently included in the oscillation theory, which has recently seen significant growth and development. For instance, you can find delay equations in [8][9][10][11], mixed equations in [12][13][14][15][16], and neutral equations in [17][18][19][20].…”

Section: Introductionmentioning

confidence: 99%

Fourth-Order Neutral Differential Equation: A Modified Approach to Optimizing Monotonic Properties

Nabih,

Moaaz,

Askar

et al. 2023

Mathematics

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In this article, we investigate some qualitative properties of solutions to a class of functional differential equations with multi-delay. Using a modified approach, we first derive a number of optimized relations and inequalities that relate the solution xs to its corresponding function zs and its derivatives. After classifying the positive solutions, we follow the Riccati approach and principle of comparison, where fourth-order differential equations are compared with first-order differential equations to obtain conditions that exclude the positive solutions. Then, we introduce new oscillation conditions. With regard to previous relevant results, our results are an extension and complement to them. This work has theoretical significance in that it uncovers some new relationships that aid in developing the oscillation theory of higher-order equations in addition to the applied relevance of neutral differential equations.

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Second-Order Non-Canonical Neutral Differential Equations with Mixed Type: Oscillatory Behavior

Cited by 2 publications

References 19 publications

An Improved Approach to Investigate the Oscillatory Properties of Third-Order Neutral Differential Equations

An Improved Approach to Investigate the Oscillatory Properties of Third-Order Neutral Differential Equations

Fourth-Order Neutral Differential Equation: A Modified Approach to Optimizing Monotonic Properties

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