Exact solutions to the space-time fraction Whitham–Broer–Kaup equation

2020 ◽  
Vol 34 (16) ◽  
pp. 2050178
Author(s):  
Damin Cao ◽  
Cheng Li ◽  
Fajiang He
Keyword(s):  
Differential Equation ◽  
Ordinary Differential Equation ◽  
Fractional Derivative ◽  
Exact Solutions ◽  
Space Time ◽  
Polynomial Discriminant

The objective work of this paper is to transform the nonlinear space-time fraction Whitham–Broer–Kaup equation into ordinary differential equation by using the conformal fractional derivative, and find the exact solutions through the complete polynomial discriminant system. At the same time, we build the appropriate solution for the identified parameters to show the existence of the solution. In addition, we provide the 3D and 2D graphics to show that the solutions are real and effective.

scholarly journals Symmetry properties and exact solutions of the time fractional Kolmogorov-Petrovskii-Piskunov equation

2019 ◽  
Vol 65 (5 Sept-Oct) ◽  
pp. 529 ◽  
Author(s):  
M. S. Hasheim ◽  
M. Inc ◽  
M. Bayram
Keyword(s):  
Differential Equation ◽  
Ordinary Differential Equation ◽  
Fractional Derivative ◽  
Exact Solutions ◽  
Lie Symmetry ◽  
Conformable Fractional Derivative ◽  
Symmetry Approach ◽  
Simplest Equation Method ◽  
Symmetry Properties ◽  
Lie Symmetry Approach

In this paper, the time fractional Kolmogorov-Petrovskii-Piskunov (FKP) equation is analyzed by means of Lie symmetry approach. The FKP is reduced to ordinary differential equation of fractional order via the attained point symmetries. Moreover, the simplest equation method is used in construct the exact solutions of underlying equation with recently introduced conformable fractional derivative.

Regarding Rational Exponential and Hyperbolic Functions Solutions of Conformable Time-Fractional Phi-four Equation

2018 ◽  
Author(s):  
Asim Zafar ◽  
Alper Korkmaz ◽  
Bushra Khalid ◽  
Hadi Rezazadeh
Keyword(s):  
Differential Equation ◽  
Ordinary Differential Equation ◽  
Fractional Derivative ◽  
Exact Solutions ◽  
Function Method ◽  
Wave Transformation ◽  
Hyperbolic Function ◽  
Hyperbolic Functions ◽  
Hyperbolic Function Method ◽  
Projected Methods

In this study, we actually want to explore the time-fractional Phi-four equation via two methods, the exp a function method and the hyperbolic function method. We transform a fractional order dierential equation into an ordinary differential equation using a wave transformation and the fractional derivative in conformable form. Then, the resulting equation has successfully been explored for new explicit exact solutions. The procured solutions are simply showed the effectiveness and plainness of the projected methods.

scholarly journals The Cauchy Problem for the Generalized Hyperbolic Novikov–Veselov Equation via the Moutard Symmetries

Symmetry ◽  
2020 ◽  
Vol 12 (12) ◽  
pp. 2113
Author(s):  
Alla A. Yurova ◽  
Artyom V. Yurov ◽  
Valerian A. Yurov
Keyword(s):  
Differential Equation ◽  
Ordinary Differential Equation ◽  
Cauchy Problem ◽  
Exact Solutions ◽  
Airy Function ◽  
The Real ◽  
The Cauchy Problem

We begin by introducing a new procedure for construction of the exact solutions to Cauchy problem of the real-valued (hyperbolic) Novikov–Veselov equation which is based on the Moutard symmetry. The procedure shown therein utilizes the well-known Airy function Ai(ξ) which in turn serves as a solution to the ordinary differential equation d2zdξ2=ξz. In the second part of the article we show that the aforementioned procedure can also work for the n-th order generalizations of the Novikov–Veselov equation, provided that one replaces the Airy function with the appropriate solution of the ordinary differential equation dn−1zdξn−1=ξz.

scholarly journals Exact Solutions for the Conformable Space-Time Fractional Zeldovich Equation with Time-Dependent Coefficients

2020 ◽  
Vol 2020 ◽  
pp. 1-6
Author(s):  
Sami Injrou
Keyword(s):  
Fractional Derivative ◽  
Exact Solutions ◽  
Combustion Process ◽  
Variable Coefficients ◽  
Space Time ◽  
Time Dependent ◽  
Conformable Fractional Derivative ◽  
Fractional Partial Differential Equations ◽  
Rational Solutions ◽  
Different Types

The aim of this paper is to improve a sub-equation method to solve the space-time fractional Zeldovich equation with time-dependent coefficients involving the conformable fractional derivative. As result, we obtain three families of solutions including the hyperbolic, trigonometric, and rational solutions. These solutions may be helpful to explain several phenomena in chemistry, including the combustion process. The study shows that the used method is effective and reliable and can be utilized as a substitution to construct new solutions of different types of nonlinear conformable fractional partial differential equations (NFPDEs) with variable coefficients.

EXPLICIT AND EXACT SOLUTIONS TO THE mKdV-SINE-GORDON EQUATION

2008 ◽  
Vol 22 (15) ◽  
pp. 1471-1485 ◽  
Author(s):  
YUANXI XIE
Keyword(s):  
Differential Equation ◽  
Ordinary Differential Equation ◽  
Exact Solutions ◽  
Gordon Equation ◽  
Variable Separation ◽  
Sine Gordon Equation ◽  
Simple Manner

By introducing an auxiliary ordinary differential equation and solving it by the method of variable separation, rich types of explicit and exact solutions of the mKdV-sine-Gordon equation are presented in a simple manner.

EXPLICIT EXACT SOLUTIONS TO THE (2+1) DIMENSIONAL SINH-POISSON EQUATION

2010 ◽  
Vol 24 (17) ◽  
pp. 3395-3409
Author(s):  
YUANXI XIE ◽  
SHIYU PENG
Keyword(s):  
Differential Equation ◽  
Ordinary Differential Equation ◽  
Exact Solutions ◽  
Poisson Equation ◽  
Variable Separation ◽  
Simple Manner

By introducing an auxiliary ordinary differential equation and solving it by the method of variable separation, many explicit exact solutions of the (2+1) dimensional sinh-Poisson equation are presented in a simple manner.

scholarly journals A solution method for integro-differential equations of conformable fractional derivative

2018 ◽  
Vol 22 (Suppl. 1) ◽  
pp. 7-14 ◽  
Author(s):  
Mustafa Bayram ◽  
Veysel Hatipoglu ◽  
Sertan Alkan ◽  
Sebahat Das
Keyword(s):  
Differential Equation ◽  
Approximate Solution ◽  
Fractional Derivative ◽  
Exact Solutions ◽  
Fractional Derivatives ◽  
Solution Method ◽  
Approximate Solutions ◽  
Conformable Fractional Derivative ◽  
Conformable Derivative ◽  
Numerical Examples

The aim of this work is to determine an approximate solution of a fractional order Volterra-Fredholm integro-differential equation using by the Sinc-collocation method. Conformable derivative is considered for the fractional derivatives. Some numerical examples having exact solutions are approximately solved. The comparisons of the exact and the approximate solutions of the examples are presented both in tables and graphical forms.

scholarly journals Explicit Exact Solutions of Space-time Fractional Drinfel’d-Sokolov-Wilson Equations

2021 ◽  
Vol 2068 (1) ◽  
pp. 012005
Author(s):  
Hongkua Lin
Keyword(s):  
Partial Differential Equations ◽  
Fractional Derivative ◽  
Exact Solutions ◽  
Rational Function ◽  
Expansion Method ◽  
Space Time ◽  
Wave Transformation ◽  
Conformable Fractional Derivative ◽  
Fractional Partial Differential Equations ◽  
Function Type

Abstract The space-time fractional Drinfel’d-Sokolov-Wilson equations (DSWEs) has attracted many researchers’ attention in recent years. In this study, combining the (G’/G,1/G)-expansion method and a fractional wave transformation, we derive abundant explicit exact solutions of the DSWEs with the conformable fractional derivative. All of the resulting solutions include triangle, hyperbolic and rational function type. It shows this technique is effective and reliable to find exact solutions of other similar nonlinear fractional partial differential equations (NFPDEs).

scholarly journals SOLITARY WAVE SOLUTIONS FOR SPACE-TIME FRACTIONAL COUPLED INTEGRABLE DISPERSIONLESS SYSTEM VIA GENERALIZED KUDRYASHOV METHOD

2021 ◽  
pp. 1439
Author(s):  
Ahmed Gaber ◽  
Hijaz Ahmad
Keyword(s):  
Solitary Wave ◽  
Fractional Derivative ◽  
Exact Solutions ◽  
Space Time ◽  
Solitary Wave Solutions ◽  
Numerical Tests ◽  
Wave Solutions ◽  
Generalized Kudryashov Method ◽  
Kudryashov Method ◽  
Fractional System

In this article, space-time fractional coupled integrable dispersionless system is considered, and we use fractional derivative in the sense of modified Riemann-Liouville. The fractional system has reduced to an ordinary differential system by fractional transformation and the generalized Kudryashov method is applied to obtain exact solutions. We also testify performance as well as precision of the applied method by means of numerical tests for obtaining solutions. The obtained results have been graphically presented to show the properties of the solutions.

Sign in / Sign up

Export Citation Format

Share Document