Fourth-order neutral dynamic equations oscillate on timescales with different arguments

Abdelkader Moumen; Amin Benaissa Cherif; Fatima Zohra Ladrani; Keltoum Bouhali; Mohamed Bouye; Abdelkader Moumen; Amin Benaissa Cherif; Fatima Zohra Ladrani; Keltoum Bouhali; Mohamed Bouye

doi:10.3934/math.20241197

AIMS Mathematics

2024, Volume 9, Issue 9: 24576-24589. doi: 10.3934/math.20241197

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Fourth-order neutral dynamic equations oscillate on timescales with different arguments

1.
Department of Mathematics, College of Science, University of Ha'il, Ha'il 55473, Saudi Arabia; Email: mo.abdelkader@uoh.edu.sa
2.
Department of Mathematics, Faculty of Mathematics and Informatics, University of Science and Technology of Oran Mohamed-Boudiaf (USTOMB), El Mnaouar, BP 1505, Bir El Djir, Oran, 31000, Algeria; Email: amin.benaissacherif@univ-usto.dz
3.
Department of Exact Sciences, Higher Training Teacher's School of Oran Ammour Ahmed (ENSO), Oran, 31000, Algeria; Email: f.z.ladrani@gmail.com
4.
Department of Mathematics, College of Science, Qassim University, Saudi Arabia; Email: k.bouhali@qu.edu.sa
5.
Department of Mathematics, College of Science, King Khalid University, P.O. Box 9004, Abha 61413, Saudi Arabia; Email: mbmahmad@kku.edu.sa

Received: 06 June 2024 Revised: 31 July 2024 Accepted: 13 August 2024 Published: 21 August 2024
MSC : 26E70, 34C10, 34K40

The theory of neutral dynamic equations on timescales was based to unify the study of differential and difference equations. The article described several oscillating criteria that will be developed for fourth-order-neutral dynamic equations in the presence of various types of arguments on timescales. The goal was to establish all necessary conditions for the solutions of these models to be oscillatory. To construct observation values, ideas from [Y. Sui and Z. Han, Oscillation of second order neutral dynamic equations with deviating arguments on time scales, Adv. Differ. Equ., 10 (2018)] were used. The research seeked to provide sufficient criteria that ensured the oscillation of solutions to these complex dynamic equations using a technique Riccati transformations generalized, emphasizing their importance in the study of oscillatory processes within various scientific and engineering contexts.
- timescales,
- oscillation,
- neutral,
- deviating arguments,
- nonlinear equations
Citation: Abdelkader Moumen, Amin Benaissa Cherif, Fatima Zohra Ladrani, Keltoum Bouhali, Mohamed Bouye. Fourth-order neutral dynamic equations oscillate on timescales with different arguments[J]. AIMS Mathematics, 2024, 9(9): 24576-24589. doi: 10.3934/math.20241197

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Abstract

The theory of neutral dynamic equations on timescales was based to unify the study of differential and difference equations. The article described several oscillating criteria that will be developed for fourth-order-neutral dynamic equations in the presence of various types of arguments on timescales. The goal was to establish all necessary conditions for the solutions of these models to be oscillatory. To construct observation values, ideas from [Y. Sui and Z. Han, Oscillation of second order neutral dynamic equations with deviating arguments on time scales, Adv. Differ. Equ., 10 (2018)] were used. The research seeked to provide sufficient criteria that ensured the oscillation of solutions to these complex dynamic equations using a technique Riccati transformations generalized, emphasizing their importance in the study of oscillatory processes within various scientific and engineering contexts.

References

[1]	C. W. J. Granger, Investigating causal relations by econometric models and cross-spectral methods, Econometrica, 37 (1969), 424. https://doi.org/10.2307/1912791 doi: 10.2307/1912791
[2]	B. Gourevitch, R. L. B. Jeanne, G. Faucon, Linear and nonlinear causality between signals: Methods, examples and neurophysiological application, Biol. Cybern., 95 (2006), 349–369. https://doi.org/10.1007/s00422-006-0098-0 doi: 10.1007/s00422-006-0098-0
[3]	S. Hilger, Ein Maßkettenak$\ddot{u}$l mit anwendung auf zentrumsannigfaltigkeiten, PhD thesis, Universität Würzburg, 1988.
[4]	M. Bohner, A. Peterson, Dynamic equations on timescales, an introduction with applications, Boston: Birkäuser, 2001. https://doi.org/10.1007/978-1-4612-0201-1
[5]	M. Bohner, A. Peterson, Advences in dynamic equations on time scales, Boston: Springer Science & Business Media, 2003. http://dx.doi.org/10.1007/978-0-8176-8230-9
[6]	A. Beniani, A. B. Cherif, F. Z. Ladrani, K. Zennir, Oscillation theorems for higher order nonlinear functional dynamic equations with unbounded neutral coefficients on timescales, Novi. Sad. J. Math., 53 (2023), 17–30.
[7]	S. G. Georgiev, K. Zennir, Boundary value problems on timescales, Chapman: Hall/CRC, 1 (2021), 692.
[8]	S. G. Georgiev, K. Zennir, Differential equations: Projector analysis on timescales, Walter de Gruyter GmbH & Co KG, 2020.
[9]	J. Džurina, I. Jadlovska, I. P. Stavroulakis, Oscillatory results for second-order non-canonical delay differential equations, Opusc. Math., 39 (2019), 483–495.
[10]	M. Zhang, W. Chen, M. Sheikh, R. A. Sallam, A. Hassan, T. Li, Oscillation criteria for second-order nonlinear delay dynamic equations of neutral type, Adv. Differ. Equ., 9 (2018). https://doi.org/10.1186/s13662-018-1474-5 doi: 10.1186/s13662-018-1474-5
[11]	S. R. Grace, J. Džurina, I. Jadlovská, T. Li, On the oscillation of fourth-order delay differential equations, Adv. Differ. Equ., 118 (2019). https://doi.org/10.1186/s13662-019-2060-1 doi: 10.1186/s13662-019-2060-1
[12]	Y. Sui1, Z. Han, Oscillation of second order neutral dynamic equations with deviating arguments on timescales, Adv. Differ. Equ., 10 (2018). https://doi.org/10.1186/s13662-018-1773-x doi: 10.1186/s13662-018-1773-x
[13]	S. Zitouni, A. Ardjouni, K. Zennir, A. Djoudi, Existence of periodic solutions in shifts $\delta$ for totally nonlinear neutral dynamic equations on timescales, ROMAI J., 15 (2019), 163–178.
[14]	A. B. Cherif, B. Bendouma, K. Zennir, S. G. Georgiev, K. Bouhali, T. Radwan, Applications of structural Nabla derivatives on timescales to dynamic equations, Mathematics, 11 (2024), 1688. https://doi.org/10.3390/math12111688 doi: 10.3390/math12111688
[15]	C. Tunç, On the asymptotic behavior of solutions of certain third-order nonlinear differential equations, Ⅰ. Int. J. Stoch. Anal., 1 (2005), 29–35. https://doi.org/10.1155/JAMSA.2005.29 doi: 10.1155/JAMSA.2005.29
[16]	M. Bohner, S. R. Grace, I. Jadlovská, Oscillation criteria for second-order neutral delay differential equations, Electron. J. Qual. Theo., 12 (2017), 1–12. https://doi.org/10.14232/ejqtde.2017.1.60 doi: 10.14232/ejqtde.2017.1.60
[17]	J. Džurina, B. Baculíková, I. Jadlovská, Oscillation of solutions to fourth-order trinomial delay differential equations, Electron. J. Differ. Eq., 70 (2015), 1–10.
[18]	T. Kusano, J. V. Manojlovic, Precise asymptotic behavior of regularly varying solutions of second order half-linear differential equations, Electron. J. Qual. Theo., 62 (2016), 1–24. https://doi.org/10.14232/ejqtde.2016.1.62 doi: 10.14232/ejqtde.2016.1.62
[19]	A. B. Trajkovic, J. V. Manojlovic, Asymptotic behavior of intermediate solutions of Fourth-order nonlinear differential equations with regularly varying coefficients, Electron. J. Differ. Eq., 129 (2016), 1–32.

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