An Improved Relationship between the Solution and Its Corresponding Function in Fourth-Order Neutral Differential Equations and Its Applications-Reference-Cited by-同舟云学术

An Improved Relationship between the Solution and Its Corresponding Function in Fourth-Order Neutral Differential Equations and Its Applications

Published:2023-04-03 Issue:7 Volume:11 Page:1708
ISSN:2227-7390
Container-title:Mathematics
language:en
Short-container-title:Mathematics

Author:

Moaaz Osama¹²^ORCID,Cesarano Clemente³,Almarri Barakah⁴^ORCID

Affiliation:

1. Department of Mathematics, College of Science, Qassim University, P.O. Box 6644, Buraydah 51452, Saudi Arabia

2. Department of Mathematics, Faculty of Science, Mansoura University, Mansoura 35516, Egypt

3. Section of Mathematics, International Telematic University Uninettuno, CorsoVittorio Emanuele II, 39, 00186 Roma, Italy

4. Department of Mathematical Sciences, College of Sciences, Princess Nourah Bint Abdulrahman University, P.O. Box 84428, Riyadh 11671, Saudi Arabia

Abstract

This work aims to derive new inequalities that improve the asymptotic and oscillatory properties of solutions to fourth-order neutral differential equations. The relationships between the solution and its corresponding function play an important role in the oscillation theory of neutral differential equations. Therefore, we improve these relationships based on the modified monotonic properties of positive solutions. Additionally, we set new conditions that confirm the absence of positive solutions and thus confirm the oscillation of all solutions of the considered equation. We finally explain the importance of the new inequalities by applying our results to some special cases of the studied equation, as well as comparing them with previous results in the literature.

Funder

Princess Nourah bint Abdulrahman University

Publisher

MDPI AG

Subject

General Mathematics,Engineering (miscellaneous),Computer Science (miscellaneous)

Link

https://www.mdpi.com/2227-7390/11/7/1708/pdf

Reference46 articles.

1. Oldham, K., and Spanier, J. (1974). The Fractional Calculus Theory and Applications of Differentiation and Integration to Arbitrary Order, Elsevier.

2. Samko, S.G., Kilbas, A.A., and Marichev, O.I. (1993). Fractional Integrals and Derivatives, Gordon and Breach Science Publishers.

3. Hale, J.K. (1971). Oxford Applied Mathematical Sciences, Springer.

4. Rihan, F.A. (2021). Delay Differential Equations and Applications to Biology, Springer Nature Singapore Pte Ltd.

5. Ladde, G.S., Lakshmikantham, V., and Zhang, B.G. (1987). Oscillation Theory of Differential Equations with Deviating Arguments, Marcel Dekker.

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