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Research Article | Open Access

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

Department of Mathematics, College of Science, University of Ha'il, Ha'il 55473, Saudi Arabia; Email: mo.abdelkader@uoh.edu.sa
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
Department of Exact Sciences, Higher Training Teacher's School of Oran Ammour Ahmed (ENSO), Oran, 31000, Algeria; Email: f.z.ladrani@gmail.com
Department of Mathematics, College of Science, Qassim University, Saudi Arabia; Email: k.bouhali@qu.edu.sa
Department of Mathematics, College of Science, King Khalid University, P.O. Box 9004, Abha 61413, Saudi Arabia; Email: mbmahmad@kku.edu.sa
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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.

CLC number: 26E70, 34C10, 34K40

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AIMS Mathematics
Pages 24576-24589

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Cite this article:
Moumen A, Cherif AB, Ladrani FZ, et al. Fourth-order neutral dynamic equations oscillate on timescales with different arguments. AIMS Mathematics, 2024, 9(9): 24576-24589. https://doi.org/10.3934/math.20241197

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Received: 06 June 2024
Revised: 31 July 2024
Accepted: 13 August 2024
Published: 15 September 2024
©2024 the Author(s), licensee AIMS Press.

This is an open access article distributed under the terms of the Creative Commons Attribution License (https://creativecommons.org/licenses/by/4.0)