scholarly journals Two Reliable Techniques for Solving Conformable Space-Time Fractional PHI-4 Model Arising in Nuclear Physics via β-derivative

2021 ◽  
Vol 67 (5 Sep-Oct) ◽  
Author(s):  
Berfin Elma ◽  
Emine Mısırlı
Keyword(s):  
Differential Equations ◽  
Nuclear Physics ◽  
Traveling Wave Solutions ◽  
First Integral ◽  
Space Time ◽  
First Integral Method ◽  
Functional Variable ◽  
Functional Variable Method ◽  
Complex Phenomena ◽  
Physical Phenomena

Nowadays,  nonlinear fractional partial differential equations have been highly using for modelling of physical phenomena. Therefore, it is very important to achieve exact solutions of fractional differential equations for understanding complex phenomena in mathematical physics. In this study,  new exact traveling wave solutions are reached of space-time fractional Phi-4 equation indicated by Atangana’s conformable derivative using two powerful different techniques. These are the functional variable method and the first integral method. Obtaining new solutions of this equation show that method is effective to understanding other nonlinear complex problems in particle and nuclear physics.

scholarly journals New Exact Solutions of Some Nonlinear Systems of Partial Differential Equations Using the First Integral Method

2013 ◽  
Vol 2013 ◽  
pp. 1-13 ◽  
Author(s):  
Shoukry Ibrahim Atia El-Ganaini
Keyword(s):  
Partial Differential Equations ◽  
Nonlinear Systems ◽  
Differential Equations ◽  
Integral Method ◽  
Traveling Wave Solutions ◽  
First Integral ◽  
First Integrals ◽  
Partial Differential ◽  
First Integral Method ◽  
New Exact Solutions

The first integral method introduced by Feng is adopted for solving some important nonlinear systems of partial differential equations, including classical Drinfel'd-Sokolov-Wilson system (DSWE), (2 + 1)-dimensional Davey-Stewartson system, and generalized Hirota-Satsuma coupled KdV system. This method provides polynomial first integrals for autonomous planar systems. Through the established first integrals, exact traveling wave solutions are formally derived in a concise manner. This method can also be applied to nonintegrable equations as well as integrable ones.

The First Integral Method for Exact Solutions of Nonlinear Fractional Differential Equations

2015 ◽  
Vol 10 (2) ◽  
Author(s):  
Ahmet Bekir ◽  
Özkan Güner ◽  
Ömer Ünsal
Keyword(s):  
Differential Equations ◽  
Exact Solutions ◽  
Fractional Differential Equations ◽  
Integral Method ◽  
First Integral ◽  
Space Time ◽  
First Integral Method ◽  
Nonlinear Fractional Differential Equations ◽  
Fractional Complex Transform ◽  
Fractional Differential

In this paper, we establish exact solutions for some nonlinear fractional differential equations (FDEs). The first integral method with help of the fractional complex transform (FCT) is used to obtain exact solutions for the time fractional modified Korteweg–de Vries (fmKdV) equation and the space–time fractional modified Benjamin–Bona–Mahony (fmBBM) equation. This method is efficient and powerful in solving kind of other nonlinear FDEs.

scholarly journals New optical solitons of conformable resonant nonlinear Schrödinger’s equation

Open Physics ◽  
2020 ◽  
Vol 18 (1) ◽  
pp. 761-769
Author(s):  
Hadi Rezazadeh ◽  
Reza Abazari ◽  
Mostafa M. A. Khater ◽  
Mustafa Inc ◽  
Dumitru Baleanu
Keyword(s):  
Evolution Equations ◽  
Traveling Wave Solutions ◽  
First Integral ◽  
Travelling Wave ◽  
Nonlinear Evolution Equations ◽  
Schrödinger’S Equation ◽  
Wave Solutions ◽  
Functional Variable ◽  
Functional Variable Method ◽  
Schrödinger's Equation

AbstractSardar subequation approach, which is one of the strong methods for solving nonlinear evolution equations, is applied to conformable resonant Schrödinger’s equation. In this technique, if we choose the special values of parameters, then we can acquire the travelling wave solutions. We conclude that these solutions are the solutions obtained by the first integral method, the trial equation method, and the functional variable method. Several new traveling wave solutions are obtained including generalized hyperbolic and trigonometric functions. The new derivation is of conformable derivation introduced by Atangana recently. Solutions are illustrated with some figures.

scholarly journals The first integral method and traveling wave solutions to Davey–Stewartson equation

2012 ◽  
Vol 17 (2) ◽  
pp. 182-193 ◽  
Author(s):  
Hossein Jafari ◽  
Atefe Sooraki ◽  
Yahya Talebi ◽  
Anjan Biswas
Keyword(s):  
Exact Solutions ◽  
Soliton Solution ◽  
Commutative Algebra ◽  
Traveling Wave ◽  
Integral Method ◽  
Traveling Wave Solutions ◽  
First Integral ◽  
First Integral Method ◽  
Wave Solutions

In this paper, the first integral method will be applied to integrate the Davey–Stewartson’s equation. Using this method, a few exact solutions will be obtained using ideas from the theory of commutative algebra. Finally, soliton solution will also be obtained using the traveling wave hypothesis.

First integral method for non-linear differential equations with conformable derivative

2018 ◽  
Vol 13 (1) ◽  
pp. 14 ◽  
Author(s):  
H. Yépez-Martínez ◽  
J.F. Gómez-Aguilar ◽  
Abdon Atangana
Keyword(s):  
Differential Equations ◽  
Exact Solutions ◽  
Integral Method ◽  
General Scheme ◽  
First Integral ◽  
Fractional Partial Differential Equations ◽  
Conformable Derivative ◽  
First Integral Method ◽  
Analytic Treatment ◽  
Linear Differential

In this paper, we present an analysis based on the first integral method in order to construct exact solutions of the nonlinear fractional partial differential equations (FPDE) described by beta-derivative. A general scheme to find the approximated solutions of the nonlinear FPDE is showed. The results obtained showed that the first integral method is an efficient technique for analytic treatment of nonlinear beta-derivative FPDE.

Analytical Approach for the Space-time Nonlinear Partial Differential Fractional Equation

2014 ◽  
Vol 15 (7-8) ◽  
Author(s):  
Ahmet Bekir ◽  
Özkan Güner
Keyword(s):  
Function Method ◽  
Analytical Approach ◽  
Fractional Derivatives ◽  
Space Time ◽  
Variable Method ◽  
Partial Differential ◽  
Functional Variable ◽  
Liouville Derivative ◽  
Functional Variable Method ◽  
Fractional Equation

AbstractIn this paper, the fractional derivatives in the sense of modified Riemann–Liouville derivative and the functional variable method, exp-function method and

scholarly journals Exact solutions of the Kudryashov–Sinelshchikov equation and nonlinear telegraph equation via the first integral method

2012 ◽  
Vol 17 (4) ◽  
pp. 481-488 ◽  
Author(s):  
Mohammad Mirzazadeh ◽  
Mostafa Eslami
Keyword(s):  
Exact Solutions ◽  
Commutative Algebra ◽  
Traveling Wave ◽  
Integral Method ◽  
Traveling Wave Solutions ◽  
First Integral ◽  
Telegraph Equation ◽  
First Integral Method ◽  
Wave Solutions ◽  
Nonlinear Telegraph Equation

In this article we find the exact traveling wave solutions of the Kudryashov–Sinelshchikov equation and nonlinear telegraph equation by using the first integral method. This method is based on the theory of commutative algebra. This method can be applied to nonintegrable equations as well as to integrable ones.

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