Neutral Differential Equations of Higher-Order in Canonical Form: Oscillation Criteria

Alsharidi, Abdulaziz Khalid; Muhib, Ali; Elagan, S. K.

doi:10.3390/math11153300

Mathematics

2023

DOI: 10.3390/math11153300

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Neutral Differential Equations of Higher-Order in Canonical Form: Oscillation Criteria

Abdulaziz Khalid Alsharidi

Ali Muhib

S. K. Elagan

Abstract: This paper aims to study a class of neutral differential equations of higher-order in canonical form. By using the comparison technique, we obtain sufficient conditions to ensure that the studied differential equations are oscillatory. The criteria that we obtained are to improve and extend some of the results in previous literature. In addition, an example is given that shows the applicability of the results we obtained.

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2024

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Cited by 4 publications

References 23 publications

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Advanced Differential Equations with Canonical Operators: New Criteria for the Oscillation

Bazighifan,

Alshammari,

Al-Ghafri

et al. 2024

Fractal Fract

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In this study, we use the integral averaging methodology, comparison with second-order differential equations, and the Riccati technique to determine the Philos-type and Hille–Nehari-type oscillation conditions of fourth-order advanced differential equations with canonical operators. In essence, these techniques supplement and generalize a wide range of established oscillation conditions. Two instance cases demonstrate the importance of our outcomes and their significant improvement.

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Advanced Differential Equations with Canonical Operators: New Criteria for the Oscillation

Bazighifan,

Alshammari,

Al-Ghafri

et al. 2024

Fractal Fract

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Forced-Perturbed Fractional Differential Equations of Higher Order: Asymptotic Properties of Non-Oscillatory Solutions

Grace,

Chhatria,

Kaleeswari

et al. 2024

Fractal Fract

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This study investigates the asymptotic behavior of non-oscillatory solutions to forced-perturbed fractional differential equations with the Caputo fractional derivative. The main aim is to unify the Beta Integral Lemma (Lemma 2) and the Gamma Integral Lemma (Lemma 3) into a single framework. By combining these two powerful tools, we propose new criteria that effectively characterize the asymptotic behavior of non-oscillatory solutions to the given equations. The analysis of such solutions has significant implications in the fields of oscillation and stability theory. Notably, our findings extend prior work by exploring a wider range of equations with more general functions and coefficients, thereby broadening the applicability and deepening the understanding of both asymptotic and oscillatory behaviors. Moreover, the criteria we introduce offer improvements over previous approaches, as demonstrated by the example provided, which highlights the advantages of our results in comparison to earlier methods.

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Differential Equations of Fourth-Order with p-Laplacian-like Operator: Oscillation Theorems

Bazighifan,

Alshammari,

Al-Ghafri

et al. 2024

Mathematics

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In this work, we find new oscillation criteria for fourth-order advanced differential equations with a p-Laplace-type operator. We established our results through a comparison method with integral averaging and Riccati techniques to obtain new oscillatory properties for the considered equation. Our criteria substantially simplify and complement a number of existing ones. We give some examples to illustrate the significance of the obtained results.

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Neutral Differential Equations of Higher-Order in Canonical Form: Oscillation Criteria

Cited by 4 publications

References 23 publications

Advanced Differential Equations with Canonical Operators: New Criteria for the Oscillation

Advanced Differential Equations with Canonical Operators: New Criteria for the Oscillation

Forced-Perturbed Fractional Differential Equations of Higher Order: Asymptotic Properties of Non-Oscillatory Solutions

Differential Equations of Fourth-Order with p-Laplacian-like Operator: Oscillation Theorems

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