Traveling wave solution of fractional KdV-Burger-Kuramoto equation describing nonlinear physical phenomena

Gupta, A. K.; Ray, S. Saha

doi:10.1063/1.4895910

Cited by 19 publications

(14 citation statements)

References 10 publications

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“…The exact solution for this problem is u(x, t) = t 2α cos(x) Γ (1+2α) , given in [11]. Table 1 and Table 2 display the absolute errors between the approximate solution acquired using the GWGM for β = 1/2, β = 3/2, α = 1 and the exact solution of Example 1.…”

Section: Test Problemsmentioning

confidence: 99%

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An effective computational approach based on Gegenbauer wavelets for solving the time-fractional Kdv-Burgers-Kuramoto equation

Seçer

Özdemir

2019

Adv Differ Equ

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In this paper, our purpose is to present a wavelet Galerkin method for solving the time-fractional KdV-Burgers-Kuramoto (KBK) equation, which describes nonlinear physical phenomena and involves instability, dissipation, and dispersion parameters. The presented computational method in this paper is based on Gegenbauer wavelets. Gegenbauer wavelets have useful properties. Gegenbauer wavelets and the operational matrix of integration, together with the Galerkin method, were used to transform the time-fractional KBK equation into the corresponding nonlinear system of algebraic equations, which can be solved numerically with Newton’s method. Our aim is to show that the Gegenbauer wavelets-based method is efficient and powerful tool for solving the KBK equation with time-fractional derivative. In order to compare the obtained numerical results of the wavelet Galerkin method with exact solutions, two test problems were chosen. The obtained results prove the performance and efficiency of the presented method.

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Section: Test Problemsmentioning

confidence: 99%

“…But the study of the nonlinear time-fractional KBK equation is very few in the literature. In [11], Legendre wavelet method was presented to solve the fractional KBK equation. Song and Zhang used the homotopy analysis method to solve a fractional KBK equation [12].…”

Section: Introductionmentioning

confidence: 99%

An effective computational approach based on Gegenbauer wavelets for solving the time-fractional Kdv-Burgers-Kuramoto equation

Seçer

Özdemir

2019

Adv Differ Equ

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“…Very recently, in studying the fractional equations that arise in shallow water waves, authors are trying to find approximate solutions either analytically or numerically . The present work discusses the details about the results found in these works.…”

Section: Introductionmentioning

confidence: 99%

Fractional KdV and Boussenisq‐Burger's equations, reduction to PDE and stability approaches

2020

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The generalized fractional Caputo‐operator is discussed. The reduction of partial differential equations retarded or advanced with delays is obtained. The applications to the space‐time‐fractional KdV and time‐fractional Boussenisq‐Burger's equation are carried. Semi‐self‐similar SS wave solutions are obtained. That is, there exists a soliton wave propagates along a specific characteristic curve in the xt‐ plane. This may be due to the effects associated with the distributed time delay. The effects of space fractional derivative on a system are attributed to the transition states. Thus, anomalous wave transport is produced mainly near the origin.

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“…In recent years, this approach has been effectively implemented for solving many types of linear and nonlinear problems in engineering and science. A few of these works can be found in [6][7][8][9].…”

Section: Introductionmentioning

confidence: 99%

A novel attempt for finding comparatively accurate solution for sine‐Gordon equation comprising Riesz space fractional derivative

Gupta

Ray

2015

Math Methods in App Sciences

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In this paper, a numerical procedure involving Chebyshev wavelet method has been implemented for computing the approximate solution of Riesz space fractional sine-Gordon equation (SGE). Two-dimensional Chebyshev wavelet method is implemented to calculate the numerical solution of space fractional SGE. The fractional SGE is considered as an interpolation between the classical SGE (corresponding to˛D 2/ and nonlocal SGE (corresponding to˛D 1/. As a consequence, the approximate solutions of fractional SGE obtained by using Chebyshev wavelet approach were compared with those derived by using modified homotopy analysis method with Fourier transform.

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Traveling wave solution of fractional KdV-Burger-Kuramoto equation describing nonlinear physical phenomena

Cited by 19 publications

References 10 publications

An effective computational approach based on Gegenbauer wavelets for solving the time-fractional Kdv-Burgers-Kuramoto equation

An effective computational approach based on Gegenbauer wavelets for solving the time-fractional Kdv-Burgers-Kuramoto equation

Fractional KdV and Boussenisq‐Burger's equations, reduction to PDE and stability approaches

A novel attempt for finding comparatively accurate solution for sine‐Gordon equation comprising Riesz space fractional derivative

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