The generalized Kudryashov method for nonlinear space–time fractional partial differential equations of Burgers type

Gaber, Ahmed; Aljohani, Abdulrahman F.; Ebaid, Abdelhalim; Machado, J.A.T.

doi:10.1007/s11071-018-4568-4

Cited by 94 publications

(36 citation statements)

References 26 publications

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“…In this section, the generalized Kudryashov method will be introduced in detail to obtain the exact solutions of FPDEs defined by Atangana's derivative [31][32][33].…”

Section: The Generalized Kudryashov Methodsmentioning

confidence: 99%

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The generalized Kudryashov method for the nonlinear fractional partial differential equations with the beta-derivative

Gürefe

2020

Rev. Mex. Fís.

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In this article, we consider the exact solutions of the Hunter-Saxton and Schrödinger equations defined by Atangana's comformable derivative using the general Kudryashov method. Firstly, Atangana's comformable fractional derivative and its properties are included. Then, by introducing the generalized Kudryashov method, exact solutions of nonlinear fractional partial differential equations (FPDEs), which can be expressed with the comformable derivative of Atangana, are classified. Looking at the results obtained, it is understood that the generalized Kudryashov method can yield important results in obtaining the exact solutions of FPDEs containing beta-derivatives.

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“…In this section, the generalized Kudryashov method will be introduced in detail to obtain the exact solutions of FPDEs defined by Atangana's derivative [31][32][33].…”

Section: The Generalized Kudryashov Methodsmentioning

confidence: 99%

“…In this article, the effectiveness of the generalized Kudryashov method was investigated to determine the exact solutions of the FPDEs with Atangana's conformable derivatives. In some studies in the literature, this method has been applied to various nonlinear fractional problems [31][32][33].…”

Section: Introductionmentioning

confidence: 99%

The generalized Kudryashov method for the nonlinear fractional partial differential equations with the beta-derivative

Gürefe

2020

Rev. Mex. Fís.

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“…Step.2: The series form solution, V (ξ ) of equation (8) is expressed in term of ( G G ) polynomial as [21]:…”

Section: The ( G G )-Expansion Methodsmentioning

confidence: 99%

“…Due to applications mentioned above, the researchers have taken keen interest in the study of FPDEs. In this connection, several mathematicians have developed different techniques for the numerical and analytical solutions of FPDEs [1]- [8]. For example, Xu et al have extended Homotopy perturbation method (HPM) to solve PDEs of fractal order [9], [10].…”

Section: Introductionmentioning

confidence: 99%

Families of Travelling Waves Solutions for Fractional-Order Extended Shallow Water Wave Equations, Using an Innovative Analytical Method

et al. 2019

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In the present research article, an efficient analytical technique is applied for travelling waves solutions of fractional partial differential equations. The investigated problems are reduced to ordinary differential equations, by a variable transformation. The solutions of the resultant ordinary differential equations are expressed in the term of some suitable polynomials, which provide trigonometric, hyperbolic and rational function solutions with some free parameters. To confirm the reliability and novelty of the current work, the proposed method is applied for the solutions of (2+1) and (3+1)-dimensional fractionalorder extended shallow water wave equations.

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“…In recent years, several studies for the CBE with arbitrarily initial and boundary value problems have appeared in the literature. Gaber et al (2019) investigated the nonlinear spacetime fractional differential equations of Burgers' type with Kudryashov method for traveling wave solutions. The variable-order time fractional Burgers' equation was studied by Hassani and Naraghirad (2019) and they have obtained an numerical solution with optimization method.…”

Section: Introductionmentioning

confidence: 99%

Fractional transform methods for coupled system of time fractional derivatives of non-homogeneous Burgers’ equations arise in diffusive effects

Munjam

2019

Comp. Appl. Math.

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The coupled system of time fractional derivatives of non-homogeneous Burgers' equations is solved both analytically and numerically. The approximate analytical solutions of power series type are obtained by the fractional homotopy analysis transform method, which is verified numerically by the coupled fractional reduced differential transform method. Particularly, the present analytical solutions are compared with the results available in the literature for several special cases, and very excellent agreement was found. An error analysis is done to compute the average squared residual errors of those analytical approximations for other cases. The present analysis shows that the proposed technique has very excellent efficiency to give solutions with high precision. On the other hand, it is found that the optimal convergence control parameter derived here not only controls the convergence of the present solutions but also leads to identifying multiple solutions.

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The generalized Kudryashov method for nonlinear space–time fractional partial differential equations of Burgers type

Cited by 94 publications

References 26 publications

The generalized Kudryashov method for the nonlinear fractional partial differential equations with the beta-derivative

The generalized Kudryashov method for the nonlinear fractional partial differential equations with the beta-derivative

Families of Travelling Waves Solutions for Fractional-Order Extended Shallow Water Wave Equations, Using an Innovative Analytical Method

Fractional transform methods for coupled system of time fractional derivatives of non-homogeneous Burgers’ equations arise in diffusive effects

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