Fourth-order neutral dynamic equations oscillate on timescales with different arguments-Reference-Cited by-同舟云学术

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

Published:2024 Issue:9 Volume:9 Page:24576-24589
ISSN:2473-6988
Container-title:AIMS Mathematics
language:
Short-container-title:MATH

Author:

Moumen Abdelkader¹,Cherif Amin Benaissa²,Ladrani Fatima Zohra³,Bouhali Keltoum⁴,Bouye Mohamed⁵

Affiliation:

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

Abstract

<p>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, <italic>Adv. Differ. Equ.</italic>, 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.</p>

Publisher

American Institute of Mathematical Sciences (AIMS)

Reference19 articles.

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

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

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