New Improved Results for Oscillation of Fourth-Order Neutral Differential Equations

Moaaz, Osama; El-Nabulsi, Rami Ahmad; Muhib, Ali; Elagan, S. K.; Zakarya, Mohammed

doi:10.3390/math9192388

Cited by 11 publications

(7 citation statements)

References 26 publications

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“…2) is comparable to the Fisher-Kolmogorov equation when M 2 > 0 [80] and to the Swift-Hohenberg equation when M 2 < 0 [81]. Equation (3.2) is also associated with the oscillatory behaviour of 4th-order differential equations discussed largely in dynamical systems [82][83][84][85][86][87]. The sign of M 2 is very significant and influences the quantum motion of the particle and hence, the case where M 4 > 0, provides a stabilized quantum dynamics.…”

Section: Some Applications Of the Generalized Schrödinger Equationmentioning

confidence: 83%

Quantum mechanics with spatial non-local effects and position-dependent mass

El-Nabulsi

Anukool

2022

Proc. R. Soc. A.

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A new higher order Schrödinger equation characterized by a position-dependent mass is introduced based on long-range spatial kernel effects and von Roos arguments. The extended Schrödinger equation depends on the sign of the moments M k , k = 0 , 1 , 2 , … and a stabilized quantum dynamic is realized for M 2 > 0 and M 4 > 0 . We have discussed its implications in several quantum mechanical systems where more than a few were raised, mainly the emergence of the quantum Pais-Uhlenbeck and the relativistic quantum harmonic oscillators besides the complex periodic potential characterized by a PT symmetry.

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Section: Some Applications Of the Generalized Schrödinger Equationmentioning

confidence: 83%

Quantum mechanics with spatial non-local effects and position-dependent mass

El-Nabulsi

Anukool

2022

Proc. R. Soc. A.

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“…Zhang et al [6] and Li and Rogovchenko [7] developed techniques for studying oscillation in order to improve the oscillation criteria of all solutions of even-order neutral differential equations. Agarwal et al [8] and Moaaz et al [9] gave new oscillation conditions for neutral differential equations. Therefore, there are many studies on the oscillation of different orders of some differential equations in canonical and noncanonical form, see [10][11][12][13][14][15][16][17].…”

Section: Literature Reviewmentioning

confidence: 99%

New Oscillation Results of Even-Order Emden–Fowler Neutral Differential Equations

et al. 2021

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The objective of this study is to establish new sufficient criteria for oscillation of solutions of even-order delay Emden-Fowler differential equations with neutral term rıyı+mıygın−1γ′+∑i=1jqiıyγμiı=0. We use Riccati transformation and the comparison with first-order differential inequalities to obtain theses criteria. Moreover, the presented oscillation conditions essentially simplify and extend known criteria in the literature. To show the importance of our results, we provide some examples. Symmetry plays an essential role in determining the correct methods for solutions to differential equations.

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“…Higher-order DEs are frequently used in a variety of fields, including the physical sciences, solid state physics, fluid physics, quantum physics, plasma physics, optics, and electrons. According to [1][2][3][4][5][6][7][8][9][10][11][12], some physical problems, such as the thin film flow problem, electromagnetic waves, and the oscillatory wave equation, always involve DEs of the second or third-order. In addition, the authors [13] studied the numerical and asymptotic of some third-order ODEs relevant to draining and coating flows.…”

Section: Introductionmentioning

confidence: 99%

Construction of Numerical RKM-Method for Solving A Class of Twelves-Order Ordinary Differential Equations

Mechee,

Fawzi,

Abdullah

2024

Iraqi Journal of Science

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This paper constructs and generalizes the numerical Runge-Kutta-Mohammed (RKM) method for solving twelve-order ordinary differential equations (ODEs). The novel contribution of this study is the development and generalization of the numerical RKM methods for solving ODEs of the order of less than a tenth. The algebraic order conditions (OCs) for the proposed RKM method are derived up to order thirteen using Taylor expansion. Then, the constructed method has been derived from these order conditions. However, the proposed numerical RKM method has been evaluated at some implementations and compared to an existing Runge-Kutta (RK) method to determine the method's viability. Moreover, this comparison demonstrates the proposed direct method is more efficient than the classical method in terms of efficiency and accuracy. Also, numerical implementations are used to prove the efficiency and time complexity of function evaluations. This direct RKM method is a suggested technique for solving ODEs of twelve orders which has great features like a direct and efficient method. Consequently, the proposed method requires less time complexity of computation than other methods.

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New Improved Results for Oscillation of Fourth-Order Neutral Differential Equations

Cited by 11 publications

References 26 publications

Quantum mechanics with spatial non-local effects and position-dependent mass

Quantum mechanics with spatial non-local effects and position-dependent mass

New Oscillation Results of Even-Order Emden–Fowler Neutral Differential Equations

Construction of Numerical RKM-Method for Solving A Class of Twelves-Order Ordinary Differential Equations

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