scholarly journals Periodic solution to general conduction problems

2013 ◽  
Vol 17 (5) ◽  
pp. 1494-1496
Author(s):  
Gui Mu ◽  
Zhengde Dai ◽  
Jun Liu ◽  
Jie Fu
Keyword(s):  
Periodic Solution ◽  
Function Method ◽  
Solution Process ◽  
Energy Localization ◽  
Periodic Effect ◽  
Hyperbolic Cosine ◽  
Cosine Functions

In this paper, we present a modified exp-function method, where hyperbolic cosine and cosine functions are used. The hyperbolic cosine functions are responsible for energy localization while cosine functions reveal the periodic effect. A general conduction problem is used as an example to illustrate the solution process.

scholarly journals Generalized bounds for hyperbolic sine and hyperbolic cosine functions

2021 ◽  
Vol 14 (1) ◽  
Author(s):  
Ramkrishna M. Dhaigude ◽  
Yogesh J. Bagul ◽  
Vinay M. Raut
Keyword(s):  
Hyperbolic Sine ◽  
Hyperbolic Cosine ◽  
Cosine Functions

scholarly journals A short review on analytical methods for fractional equations with he’s fractional derivative

2017 ◽  
Vol 21 (4) ◽  
pp. 1567-1574 ◽  
Author(s):  
Yan Wang ◽  
Yu-Feng Zhang ◽  
Jian-Gen Liu ◽  
Muhammad Iqbal
Keyword(s):  
Fractional Derivative ◽  
Fractional Differential Equations ◽  
Analytical Methods ◽  
Function Method ◽  
Solution Process ◽  
Short Review ◽  
Fractional Equations ◽  
Generalized Kudryashov Method ◽  
Kudryashov Method ◽  
Fractional Differential

He?s fractional derivative is adopted in this paper, and analytical methods for fractional differential equations are briefly reviewed, two modifications of the exp-function method (the generalized Kudryashov method and generalized expo-nential rational function method) are emphasized, and fractional Benjamin-Bo-na-Mahony equation with He?s fractional derivative is used as an example to elucidate the solution process.

scholarly journals Almost anti-periodic solution of inertial neural networks model on time scales

2022 ◽  
Vol 355 ◽  
pp. 02006
Author(s):  
Adnène Arbi ◽  
Najeh Tahri
Keyword(s):  
Neural Networks ◽  
Periodic Solution ◽  
Lyapunov Function ◽  
Time Scales ◽  
Differential Inequality ◽  
Function Method ◽  
Lyapunov Function Method ◽  
Existence And Stability ◽  
Inertial Neural Networks ◽  
Inequality Techniques

In this work, since the importance of investigation of oscillators solutions, an methodology for proving the existence and stability of almost anti-periodic solutions of inertial neural networks model on time scales are discussed. By developing an approach based on differential inequality techniques coupled with Lyapunov function method. A numerical example is given for illustration.

EFFECT OF FRACTIONAL DERIVATIVE PROPERTIES ON THE PERIODIC SOLUTION OF THE NONLINEAR OSCILLATIONS

Fractals ◽  
2020 ◽  
Vol 28 (07) ◽  
pp. 2050095 ◽  
Author(s):  
YUSRY O. EL-DIB ◽  
NASSER S. ELGAZERY
Keyword(s):  
Periodic Solution ◽  
Fractional Derivative ◽  
Perturbation Method ◽  
Nonlinear Oscillations ◽  
Duffing Oscillator ◽  
Solution Process ◽  
Auxiliary Parameter ◽  
Periodic Force ◽  
Definition Of ◽  
Perturbed Equation

A periodic solution of the time-fractional nonlinear oscillator is derived based on the Riemann–Liouville definition of the fractional derivative. In this approach, the particular integral to the fractional perturbed equation is found out. An enhanced perturbation method is developed to study the forced nonlinear Duffing oscillator. The modified homotopy equation with two expanded parameters and an additional auxiliary parameter is applied in this proposal. The basic idea of the enhanced method is to apply the annihilator operator to construct a simplified equation freeness of the periodic force. This method makes the solution process for the forced problem much simpler. The resulting equation is valid for studying all types of possible resonance states. The outcome shows that this alteration method overcomes all shortcomings of the perturbation method and leads to obtain a periodic solution.

scholarly journals Permanence and Periodic Solutions for a Two-Patch Impulsive Migration PeriodicN-Species Lotka-Volterra Competitive System

2015 ◽  
Vol 2015 ◽  
pp. 1-14 ◽  
Author(s):  
Zijian Liu ◽  
Chenxue Yang
Keyword(s):  
Periodic Solution ◽  
Lyapunov Function ◽  
Function Method ◽  
Sufficient Conditions ◽  
Positive Periodic Solution ◽  
Analysis Method ◽  
Competitive System ◽  
Numerical Examples ◽  
Lyapunov Function Method ◽  
Globally Stable

We study a two-patch impulsive migration periodicN-species Lotka-Volterra competitive system. Based on analysis method, inequality estimation, and Lyapunov function method, sufficient conditions for the permanence and existence of a unique globally stable positive periodic solution of the system are established. Some numerical examples are shown to verify our results and discuss the model further.

scholarly journals A Kind of Infinite-Dimensional Novikov Algebras and Its Realizations

2013 ◽  
Vol 2013 ◽  
pp. 1-5 ◽  
Author(s):  
Liangyun Chen
Keyword(s):  
Infinite Dimensional ◽  
Hyperbolic Sine ◽  
Hyperbolic Cosine ◽  
Novikov Algebras ◽  
Sine Functions ◽  
Cosine Functions

We construct a kind of infinite-dimensional Novikov algebras and give its realization by hyperbolic sine functions and hyperbolic cosine functions.

scholarly journals The exact solution of the nonlinear Schrödinger equation by the exp-function method

2021 ◽  
pp. 88-88
Author(s):  
Qiaoling Chen ◽  
Zhiqiang Sun
Keyword(s):  
Exact Solution ◽  
Schrödinger Equation ◽  
Nonlinear Schrödinger Equation ◽  
Schrodinger Equation ◽  
Function Method ◽  
Solution Process ◽  
Nonlinear Schrodinger Equation ◽  
Dinger Equation ◽  
Nonlinear Schrödinger ◽  
Free Parameters

This paper elucidates the main advantages of the exp-function method in finding the exact solution of the nonlinear Schr?dinger equation. The solution process is extremely simple and accessible, and the obtained solution contains some free parameters.

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