The purpose of this article is to explore the asymptotic properties for a class of fourth-order neutral differential equations. Based on a comparison with the differential inequality of the first-order, we have provided new oscillation conditions for...
The study of the oscillatory behavior of solutions to second order nonlinear differential equations is motivated by their numerous applications in the natural sciences and engineering. In the presented research, some new oscillation criteria for a cl...
The objective of this paper is to study oscillation of fourth-order neutral differential equation. By using Riccati substitution and comparison technique, new oscillation conditions are obtained which insure that all solutions of the studied equation...
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 t...
In this work, new criteria for the oscillatory behavior of even-order delay differential equations with neutral term are established by comparison technique, Riccati transformation and integral averaging method. The presented results essentially exte...
Our interest in this paper is to study and develop oscillation conditions for solutions of a class of neutral differential equations with damping terms. New oscillation criteria were obtained by using Riccati transforms. The criteria we obtained impr...
Differential equations are useful mathematical tools for solving complex problems. Differential equations include ordinary and partial differential equations. Nonlinear equations can express the nonlinear relationship between dependent and independen...
In this research, we applied three techniques—the comparison technique, the Riccati technique, and the integral averages technique to analyze and establish various conditions and properties associated with the oscillatory behavior of even-order...
This paper presents a new numerical scheme for a class of linear impulsive neutral differential equations with constant coefficients based on the Euler method. We rigorously establish the first-order convergence of the proposed numerical approach. Ad...
The aim of this work is to study oscillatory behavior of solutions for even-order neutral nonlinear differential equations. By using the Riccati substitution, a new oscillation conditions is obtained which insures that all solutions to the studied eq...
In this study, our goal was to establish improved inequalities that enhance the asymptotic and oscillatory behaviors of solutions to even-order neutral differential equations. In the oscillation theory of neutral differential equations, the connectio...
In this paper, we aim to study the monotonic properties of the solutions of a class of neutral delay differential equations. The importance of this study lies in the fact that the monotonic properties largely control the study of the oscillation and...
We primarily investigate the existence of solutions for fractional neutral integro-differential equations with nonlocal initial conditions, which are crucial for understanding natural phenomena. Taking into account factors such as neutral type, fract...
This research investigates the oscillation criteria of nonlinear second-order neutral differential equations with multiple delays, focusing on their noncanonical forms. By leveraging an innovative iterative technique, new relationships are establishe...
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 advanc...
In this paper, we analyze the asymptotic behavior of solutions to a class of third-order neutral differential equations. Using different methods, we obtain some new results concerning the oscillation of this type of equation. Our new results compleme...
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...
This article highlights the oscillatory properties of second-order Emden–Fowler delay differential equations featuring sublinear neutral terms and multiple delays, encompassing both canonical and noncanonical cases. Through the proofs of severa...
In this paper, we study the oscillation of solutions of fourth-order neutral delay differential equations in non-canonical form. By using Riccati transformation, we establish some new oscillation conditions. We provide some examples to examine the ap...
The objective of this work is to study some new oscillation criteria for even-order differential equation with neutral term
This paper aims to study a class of neutral differential equations of higher-order in canonical form. By using the comparison technique, we obtain sufficient conditions to ensure that the studied differential equations are oscillatory. The criteria t...
We investigate the oscillation of the fourth-order differential equation for a class of functional differential equations of the neutral type. We obtain a new single-oscillation criterion for the oscillation of all the solutions of our equation. We e...
In this paper, we are concerned with a fixed stepsize Euler method for a class of linear impulsive neutral delay differential equations. By taking the partition nodes for the Euler scheme and employing the linear interpolation, we strictly prove the...
In this work, we investigate the oscillatory properties of the neutral differential equation
In this article, we study a class of non-linear neutral delay differential equations of third order. We first prove criteria for non-existence of non-Kneser solutions, and criteria for non-existence of Kneser solutions. We then use these results to p...
In this work, by considering a third-order differential equation with delay-neutral arguments, we investigate the oscillatory behavior of solutions. It is known that the relationships between the solution and its derivatives of different orders, as w...
This research deals with the study of the oscillatory behavior of solutions of second-order differential equations containing neutral conditions, both in sublinear and superlinear terms, with a focus on the noncanonical case. The research provides a...
New oscillatory properties for the oscillation of unbounded solutions to a class of third-order neutral differential equations with several deviating arguments are established. Several oscillation results are established by using generalized Riccati...
We study the second-order neutral half-linear differential equation and formulate new oscillation criteria for this equation, which are obtained through the use of the modified Riccati technique. In the first statement, the oscillation of the equatio...
In this paper, new sufficient conditions for oscillation of fourth-order neutral differential equations are established. One objective of our paper is to further improve and complement some well-known results which were published recently in the lite...
The paper is devoted to the study of oscillation of even-order neutral differential equations. New Kamenev-type oscillation criteria are established, and they essentially improve and complement some the well-known results reported in the literature....
The oscillation and asymptotic behavior of solutions of a general class of damped second-order differential equations with several sub-linear neutral terms is considered. New sufficient conditions are established to fulfill a part of the gap in the o...
This paper focuses on the problem of the pth moment and almost sure exponential stability of impulsive neutral stochastic functional differential equations (INSFDEs). Based on the Lyapunov function and average dwell time (ADT), two sufficient criteri...
The motivation for this paper is to create new criteria for oscillation of solutions of second-order nonlinear neutral differential equations. In more than one respect, our results improve several related ones in the literature. As proof of the effec...
In this paper, we investigate the existence of solutions for the fractional neutral differential equations with random impulses. The results are obtained by using Krasnoselskii’s fixed point theorem. Examples are added to show applications of the mai...
The neutral delay differential equations have many applications in the natural sciences, technology, and population dynamics. In this paper, we establish several new oscillation criteria for a kind of even-order quasi-linear neutral delay differentia...
This research focuses on studying the asymptotic and oscillatory behavior of a special class of even-order nonlinear neutral differential equations, including damping terms. The research aims to achieve qualitative progress in understanding the relat...
The main purpose of this paper is to obtain criteria for the oscillation of all solutions of a third-order half-linear neutral differential equation. The main result in this paper is an oscillation theorem obtained by comparing the equation under inv...
In this study, we aim to set new criteria regarding the asymptotic behavior of the neutral differential equation of the third order. These criteria are designed to ensure that this equation is oscillatory using comparisons with first-order differenti...
In this paper, by using the Riccati transformation and integral inequality technique, we establish several oscillation criteria for second-order Emden–Fowler neutral delay differential equations under the canonical case and non-canonical case,...
This work is concerned with the oscillatory behavior of solutions of even-order neutral differential equations. By using the technique of Riccati transformation and comparison principles with the second-order differential equations, we obtain a new P...
Based on the comparison with first-order delay equations, we establish a new oscillation criterion for a class of even-order neutral differential equations. Our new criterion improves a number of existing ones. An illustrative example is provided.
In this work, new oscillation criteria are established for a second-order differential equation with several sublinear neutral terms and in the canonical case. To determine the oscillation conditions, we followed the Riccati approach and also compare...
In this work, we will derive new asymptotic properties of the positive solutions of the fourth-order neutral differential equation with the non-canonical factor. We follow an improved approach that enables us to create oscillation criteria of an iter...
In this work, we study the oscillatory features of a class of neutral differential equations with multiple delays. We present novel oscillation conditions for this equation by using a comparison method. We create conditions that exclude the positive...
The aim of this study is to investigate the existence of solutions for a non-linear neutral differential equation with an unbounded delay. To achieve our goals, we take advantage of fixed point theorems for self-mappings satisfying a generalized (
The aim of this paper is to study the oscillatory properties of 4th-order neutral differential equations. We obtain some oscillation criteria for the equation by the theory of comparison. The obtained results improve well-known oscillation results in...
In this paper, we aimed to study some asymptotic properties of a class of third-order neutral differential equations with advanced argument in canonical form. We provide new and simplified oscillation criteria that improve and complement a number of...
In this paper, we focus on the second-order neutral differential equations with deviating arguments which are under the canonical condition. New oscillation criteria are established, which are based on a first-order delay differential equation and ge...
This paper explores the asymptotic and oscillatory properties of a class of third-order neutral differential equations with multiple delays in a non-canonical form. The main objective is to simplify the non-canonical form by converting it to a canoni...
of 5