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14 pages, 268 KiB

Open AccessArticle

Oscillation and Asymptotic Behavior of Third-Order Neutral Delay Differential Equations with Mixed Nonlinearities

by Balakrishnan Sudha, George E. Chatzarakis and Ethiraju Thandapani

Mathematics 2025, 13(5), 783; https://doi.org/10.3390/math13050783 - 27 Feb 2025

Viewed by 607

In the present article, we create new sufficient conditions for the oscillatory and asymptotic behavior of solutions of third-order nonlinear neutral delay differential equations with several super-linear and sub-linear terms. The results are obtained first by applying the arithmetic–geometric mean inequality along with [...] Read more.

In the present article, we create new sufficient conditions for the oscillatory and asymptotic behavior of solutions of third-order nonlinear neutral delay differential equations with several super-linear and sub-linear terms. The results are obtained first by applying the arithmetic–geometric mean inequality along with the linearization method and then using comparison method as well as the integral averaging technique. Finally, we show the importance and novelty of the main results by applying them to special cases of the studied equation. Full article

(This article belongs to the Section C1: Difference and Differential Equations)

19 pages, 615 KiB

Open AccessArticle

An Efficient Approach for Mixed Neutral Delay Differential Equations

by Rupal Aggarwal, Giriraj Methi, Ravi P. Agarwal and Basharat Hussain

Computation 2025, 13(2), 50; https://doi.org/10.3390/computation13020050 - 10 Feb 2025

Cited by 1 | Viewed by 737

Abstract

In this paper, neutral delay differential equations, which contain constant and proportional terms, termed mixed neutral delay differential equations, are solved numerically. Moreover, an efficient numerical approach is introduced (a combination of the method of steps and the Haar wavelet collocation method) to [...] Read more.

In this paper, neutral delay differential equations, which contain constant and proportional terms, termed mixed neutral delay differential equations, are solved numerically. Moreover, an efficient numerical approach is introduced (a combination of the method of steps and the Haar wavelet collocation method) to solve mixed neutral delay differential equations. Furthermore, we prove the existence and uniqueness theorem using successive approximation methods. Three numerical examples are presented to demonstrate the implementation of the proposed method. Furthermore, the precision and accuracy of the Haar wavelet collocation method are validated theoretically by proving that the error tends to zero as the resolution level increases, and numerically, by calculating the rate of convergence. The findings contribute to a broader application of the wavelet-based method to a more complex type of differential equation. This study offers a framework for the extension of the combination of both methods to be applied to potential real-world applications in control theory, biological models, and computational sciences. Full article

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10 pages, 291 KiB

Open AccessArticle

Oscillation of Emden–Fowler-Type Differential Equations with Non-Canonical Operators and Mixed Neutral Terms

by Sathish Kumar Marappan, Alanoud Almutairi, Loredana Florentina Iambor and Omar Bazighifan

Symmetry 2023, 15(2), 553; https://doi.org/10.3390/sym15020553 - 19 Feb 2023

Cited by 8 | Viewed by 1901

Abstract

The study of the symmetric properties of differential equations is essential for identifying effective methods for solving them. In this paper, we examine the oscillatory behavior of solutions of Emden–Fowler-type mixed non-linear neutral differential equations with both canonical and non-canonical operators. By utilizing [...] Read more.

The study of the symmetric properties of differential equations is essential for identifying effective methods for solving them. In this paper, we examine the oscillatory behavior of solutions of Emden–Fowler-type mixed non-linear neutral differential equations with both canonical and non-canonical operators. By utilizing integral conditions and the integral averaging method, we present new sufficient conditions to ensure that all solutions are oscillatory. Our results enhance and extend previous findings in the literature and are illustrated with suitable examples to demonstrate their effectiveness. Full article

10 pages, 273 KiB

Open AccessArticle

Asymptotic Behavior and Oscillation of Third-Order Nonlinear Neutral Differential Equations with Mixed Nonlinearities

by Taher S. Hassan and Bassant M. El-Matary

Mathematics 2023, 11(2), 424; https://doi.org/10.3390/math11020424 - 13 Jan 2023

Cited by 10 | Viewed by 1798

Abstract

In this paper, we investigate the asymptotic properties of third-order nonlinear neutral differential equations with mixed nonlinearities using the comparison principle. Our results not only vastly improve upon but also broadly generalize many previously known ones. Examples demonstrating the applicability and efficacy of [...] Read more.

In this paper, we investigate the asymptotic properties of third-order nonlinear neutral differential equations with mixed nonlinearities using the comparison principle. Our results not only vastly improve upon but also broadly generalize many previously known ones. Examples demonstrating the applicability and efficacy of our results are provided. Full article

(This article belongs to the Special Issue Mathematical Modeling and Simulation of Oscillatory Phenomena)

19 pages, 351 KiB

Open AccessArticle

Mixed Caputo Fractional Neutral Stochastic Differential Equations with Impulses and Variable Delay

by Mahmoud Abouagwa, Rashad A. R. Bantan, Waleed Almutiry, Anas D. Khalaf and Mohammed Elgarhy

Fractal Fract. 2021, 5(4), 239; https://doi.org/10.3390/fractalfract5040239 - 23 Nov 2021

Cited by 14 | Viewed by 2290

Abstract

In this manuscript, a new class of impulsive fractional Caputo neutral stochastic differential equations with variable delay (IFNSDEs, in short) perturbed by fractional Brownain motion (fBm) and Poisson jumps was studied. We utilized the Carathéodory approximation approach and stochastic calculus to present the [...] Read more.

In this manuscript, a new class of impulsive fractional Caputo neutral stochastic differential equations with variable delay (IFNSDEs, in short) perturbed by fractional Brownain motion (fBm) and Poisson jumps was studied. We utilized the Carathéodory approximation approach and stochastic calculus to present the existence and uniqueness theorem of the stochastic system under Carathéodory-type conditions with Lipschitz and non-Lipschitz conditions as special cases. Some existing results are generalized and enhanced. Finally, an application is offered to illustrate the obtained theoretical results. Full article

(This article belongs to the Special Issue Probabilistic Solutions and Stochastic Representation of Fractional Differential Equations)

14 pages, 374 KiB

Open AccessArticle

An Oscillation Test for Solutions of Second-Order Neutral Differential Equations of Mixed Type

by Osama Moaaz, Ali Muhib and Shyam S. Santra

Mathematics 2021, 9(14), 1634; https://doi.org/10.3390/math9141634 - 11 Jul 2021

Cited by 6 | Viewed by 2234

Abstract

It is easy to notice the great recent development in the oscillation theory of neutral differential equations. The primary aim of this work is to extend this development to neutral differential equations of mixed type (including both delay and advanced terms). In this [...] Read more.

It is easy to notice the great recent development in the oscillation theory of neutral differential equations. The primary aim of this work is to extend this development to neutral differential equations of mixed type (including both delay and advanced terms). In this work, we consider the second-order non-canonical neutral differential equations of mixed type and establish a new single-condition criterion for the oscillation of all solutions. By using a different approach and many techniques, we obtain improved oscillation criteria that are easy to apply on different models of equations. Full article

(This article belongs to the Special Issue Differential/Difference Equations: Mathematical Modeling, Oscillation and Applications)

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9 pages, 269 KiB

Open AccessArticle

Oscillation of Second-Order Differential Equations with Multiple and Mixed Delays under a Canonical Operator

by Shyam Sundar Santra, Rami Ahmad El-Nabulsi and Khaled Mohamed Khedher

Mathematics 2021, 9(12), 1323; https://doi.org/10.3390/math9121323 - 8 Jun 2021

Cited by 9 | Viewed by 2757

Abstract

In this work, we obtained new sufficient and necessary conditions for the oscillation of second-order differential equations with mixed and multiple delays under a canonical operator. Our methods could be applicable to find the sufficient and necessary conditions for any neutral differential equations. [...] Read more.

In this work, we obtained new sufficient and necessary conditions for the oscillation of second-order differential equations with mixed and multiple delays under a canonical operator. Our methods could be applicable to find the sufficient and necessary conditions for any neutral differential equations. Furthermore, we proved the validity of the obtained results via particular examples. At the end of the paper, we provide the future scope of this study. Full article

(This article belongs to the Special Issue Recent Advances in Differential Equations and Applications)

10 pages, 266 KiB

Open AccessArticle

New Aspects for Oscillation of Differential Systems with Mixed Delays and Impulses

by Shyam Sundar Santra, Khaled Mohamed Khedher and Shao-Wen Yao

Symmetry 2021, 13(5), 780; https://doi.org/10.3390/sym13050780 - 1 May 2021

Cited by 11 | Viewed by 1597

Abstract

Oscillation and symmetry play an important role in many applications such as engineering, physics, medicine, and vibration in flight. In this work, we obtain sufficient and necessary conditions for the oscillation of the solutions to a second-order differential equation with impulses and mixed [...] Read more.

Oscillation and symmetry play an important role in many applications such as engineering, physics, medicine, and vibration in flight. In this work, we obtain sufficient and necessary conditions for the oscillation of the solutions to a second-order differential equation with impulses and mixed delays when the neutral coefficient lies within

[0, 1)

. Furthermore, an examination of the validity of the proposed criteria has been demonstrated via particular examples. Full article

(This article belongs to the Special Issue Qualitative Theory and Symmetries of Ordinary Differential Equations)

9 pages, 260 KiB

Open AccessArticle

Philos-Type Oscillation Results for Third-Order Differential Equation with Mixed Neutral Terms

by Marappan Sathish Kumar, Omar Bazighifan, Alanoud Almutairi and Dimplekumar N. Chalishajar

Mathematics 2021, 9(9), 1021; https://doi.org/10.3390/math9091021 - 30 Apr 2021

Cited by 11 | Viewed by 2031

Abstract

The motivation for this paper is to create new Philos-type oscillation criteria that are established for third-order mixed neutral differential equations with distributed deviating arguments. The key idea of our approach is to use the triple of the Riccati transformation techniques and the [...] Read more.

The motivation for this paper is to create new Philos-type oscillation criteria that are established for third-order mixed neutral differential equations with distributed deviating arguments. The key idea of our approach is to use the triple of the Riccati transformation techniques and the integral averaging technique. The established criteria improve, simplify and complement results that have been published recently in the literature. An example is also given to demonstrate the applicability of the obtained conditions. Full article

8 pages, 248 KiB

Open AccessArticle

New Theorems for Oscillations to Differential Equations with Mixed Delays

by Shyam Sundar Santra, Debasish Majumder, Rupak Bhattacharjee, Omar Bazighifan, Khaled Mohamed Khedher and Marin Marin

Symmetry 2021, 13(3), 367; https://doi.org/10.3390/sym13030367 - 25 Feb 2021

Cited by 10 | Viewed by 2277

Abstract

The oscillation of differential equations plays an important role in many applications in physics, biology and engineering. The symmetry helps to deciding the right way to study oscillatory behavior of solutions of this equations. The purpose of this article is to establish new [...] Read more.

The oscillation of differential equations plays an important role in many applications in physics, biology and engineering. The symmetry helps to deciding the right way to study oscillatory behavior of solutions of this equations. The purpose of this article is to establish new oscillatory properties which describe both the necessary and sufficient conditions for a class of nonlinear second-order differential equations with neutral term and mixed delays of the form

{(p (ι) {(w^{'} (ι))}^{α})}^{'} + r (ι) u^{β} (ν (ι)) = 0, ι \geq ι_{0}

where

w (ι) = u (ι) + q (ι) u (ζ (ι)) .

Furthermore, examining the validity of the proposed criteria has been demonstrated via particular examples. Full article

(This article belongs to the Special Issue Symmetry in Nonlinear Equations: Mathematical Models, Methods and Applications)

10 pages, 267 KiB

Open AccessArticle

Second-Order Non-Canonical Neutral Differential Equations with Mixed Type: Oscillatory Behavior

by Osama Moaaz, Amany Nabih, Hammad Alotaibi and Y. S. Hamed

Symmetry 2021, 13(2), 318; https://doi.org/10.3390/sym13020318 - 14 Feb 2021

Cited by 4 | Viewed by 1966

Abstract

In this paper, we establish new sufficient conditions for the oscillation of solutions of a class of second-order delay differential equations with a mixed neutral term, which are under the non-canonical condition. The results obtained complement and simplify some known results in the [...] Read more.

In this paper, we establish new sufficient conditions for the oscillation of solutions of a class of second-order delay differential equations with a mixed neutral term, which are under the non-canonical condition. The results obtained complement and simplify some known results in the relevant literature. Example illustrating the results is included. Full article

(This article belongs to the Special Issue Symmetry in Modeling and Analysis of Dynamic Systems)

13 pages, 282 KiB

Open AccessArticle

Asymptotic Behavior of Solutions of the Third Order Nonlinear Mixed Type Neutral Differential Equations

by Osama Moaaz, Dimplekumar Chalishajar and Omar Bazighifan

Mathematics 2020, 8(4), 485; https://doi.org/10.3390/math8040485 - 1 Apr 2020

Cited by 12 | Viewed by 2396

Abstract

The objective of our paper is to study asymptotic properties of the class of third order neutral differential equations with advanced and delayed arguments. Our results supplement and improve some known results obtained in the literature. An illustrative example is provided. Full article

(This article belongs to the Special Issue Advances in Differential and Difference Equations with Applications 2020)

18 pages, 285 KiB

Open AccessArticle

A New Approach for Exponential Stability Criteria of New Certain Nonlinear Neutral Differential Equations with Mixed Time-Varying Delays

by Janejira Tranthi, Thongchai Botmart, Wajaree Weera and Piyapong Niamsup

Mathematics 2019, 7(8), 737; https://doi.org/10.3390/math7080737 - 12 Aug 2019

Cited by 4 | Viewed by 2853

Abstract

This work is concerned with the delay-dependent criteria for exponential stability analysis of neutral differential equation with a more generally interval-distributed and discrete time-varying delays. By using a novel Lyapunov–Krasovkii functional, descriptor model transformation, utilization of the Newton–Leibniz formula, and the zero equation, [...] Read more.

This work is concerned with the delay-dependent criteria for exponential stability analysis of neutral differential equation with a more generally interval-distributed and discrete time-varying delays. By using a novel Lyapunov–Krasovkii functional, descriptor model transformation, utilization of the Newton–Leibniz formula, and the zero equation, the criteria for exponential stability are in the form of linear matrix inequalities (LMIs). Finally, we present the effectiveness of the theoretical results in numerical examples to show less conservative conditions than the others in the literature. Full article

(This article belongs to the Section E3: Mathematical Biology)

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