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Mathematics
Volume 13
Issue 15
10.3390/math13152494
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This is an early access version, the complete PDF, HTML, and XML versions will be available soon.
Article

New Asymptotic and Oscillatory Results for Third-Order Noncanonical Advanced Differential Equations

by
Asma Althemairi
1,
Stefano Serra-Capizzano
2,3,*,
Belgees Qaraad
4 and
Higinio Ramos
5,6
1
Department of Mathematical Sciences, College of Science, Princess Nourah bint Abdulrahman University, P.O. Box 84428, Riyadh 11671, Saudi Arabia
2
Department of Science and High Technology, University of Insubria, Via Valleggio 11, 22100 Como, Italy
3
Division of Scientific Computing, Department of Information Technology, Uppsala University, Lägerhyddsv 2, hus 2, SE-751 05 Uppsala, Sweden
4
Department of Mathematics, Faculty of Science, Mansoura University, Mansoura 35516, Egypt
5
Scientific Computing Group, Universidad de Salamanca, Plaza de la Merced, 37008 Salamanca, Spain
6
Department of Mathematics, Escuela Politecnica Superior de Zamora, Campus Viriato, 49022 Zamora, Spain
*
Author to whom correspondence should be addressed.
Mathematics 2025, 13(15), 2494; https://doi.org/10.3390/math13152494
Submission received: 29 May 2025 / Revised: 28 July 2025 / Accepted: 30 July 2025 / Published: 3 August 2025
(This article belongs to the Special Issue Functional Differential Equations and Epidemiological Modelling, 2nd Edition)
Versions Notes

Abstract

The aim of this study is to investigate the oscillatory behaviour of a new class of third-order advanced differential equations in their noncanonical form. By employing newly refined transformations, the noncanonical equation is converted into its canonical form. This transformation reduces the number of possible nonoscillatory solution categories from four to two. The present study is based on a thorough and comprehensive review of existing literature and introduces new oscillation criteria by the comparison principle and other analytical techniques. These criteria provide sufficient conditions for the oscillation of solutions without imposing additional restrictive assumptions. The validity and significance of the obtained results are demonstrated through illustrative examples.
Keywords: oscillation; third-order; noncanonical; advanced differential equation oscillation; third-order; noncanonical; advanced differential equation

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MDPI and ACS Style

Althemairi, A.; Serra-Capizzano, S.; Qaraad, B.; Ramos, H. New Asymptotic and Oscillatory Results for Third-Order Noncanonical Advanced Differential Equations. Mathematics 2025, 13, 2494. https://doi.org/10.3390/math13152494

AMA Style

Althemairi A, Serra-Capizzano S, Qaraad B, Ramos H. New Asymptotic and Oscillatory Results for Third-Order Noncanonical Advanced Differential Equations. Mathematics. 2025; 13(15):2494. https://doi.org/10.3390/math13152494

Chicago/Turabian Style

Althemairi, Asma, Stefano Serra-Capizzano, Belgees Qaraad, and Higinio Ramos. 2025. "New Asymptotic and Oscillatory Results for Third-Order Noncanonical Advanced Differential Equations" Mathematics 13, no. 15: 2494. https://doi.org/10.3390/math13152494

APA Style

Althemairi, A., Serra-Capizzano, S., Qaraad, B., & Ramos, H. (2025). New Asymptotic and Oscillatory Results for Third-Order Noncanonical Advanced Differential Equations. Mathematics, 13(15), 2494. https://doi.org/10.3390/math13152494

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