Multi-wave solutions of the space–time fractional Burgers and Sharma–Tasso–Olver equations

Abdel-Salam, Emad A.-B.; Hassan, Gamal

doi:10.1016/j.asej.2015.04.001

Cited by 15 publications

(1 citation statement)

References 53 publications

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“…Also, the generalized differential transform method [23] and the meshfree spectral method [24] have been used to solve TFCBEs by Liu and Hou [23] and Hussain et al [24]. Furthermore, Bekir and Guner [31] solved equations ( 1)-(3) using the (G /G)-expansion method, while Abdel-Salam and Hassan [32] solved equation (1) using the generalized exp-function method. Also, there are some references [33][34][35][36][37][38] about the numerical solutions of fractional equations, the researcher should read them.…”

Section: Introductionmentioning

confidence: 99%

Parametric quintic spline for time fractional Burger’s and coupled Burgers’ equations

Hammad

Semary

Khattab

2023

Fixed Point Theory Algorithms Sci Eng

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In this paper, the numerical solutions of time fractional Burger’s and coupled Burgers’ equations are obtained using the parametric quintic spline method with a local truncation error of order eight in distance direction. Additionally, the von Neumann method was utilized for studying the stability analysis of the present method. Finally, to show the accuracy of this method, some examples with different cases for Burger’s and coupled Burgers’ equations are presented and their results are compared with the previous methods.

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Section: Introductionmentioning

confidence: 99%

Parametric quintic spline for time fractional Burger’s and coupled Burgers’ equations

Hammad

Semary

Khattab

2023

Fixed Point Theory Algorithms Sci Eng

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Numerical solutions of time and space fractional coupled Burgers equations using time–space Chebyshev pseudospectral method

Mittal

Balyan

2020

Math Methods in App Sciences

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The aim of the paper is to develop and analyze a spectrally accurate time–space pseudospectral method to the approximate solution of nonlinear time and space fractional coupled Burgers equations. Liouville–Caputo fractional derivative formula is used to evaluate the fractional derivatives matrix at CGL points. Using the Chebyshev fractional derivative matrices, the given problem is reduced to a system of nonlinear algebraic equations. A mapping is used to transform the nonhomogeneous initial–boundary values to homogeneous initial–boundary values. Error analysis of the proposed method for the equation is presented. A model example of fractional coupled Burgers equations is tested for a set of fractional‐order derivatives. For the proposed method, highly accurate numerical results are obtained, which confirm the accuracy and efficiency of the proposed method.

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Efficient numerical schemes for the solution of generalized time fractional Burgers type equations

Asgari

Hosseini

2017

Numer Algor

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Multi-wave solutions of the space–time fractional Burgers and Sharma–Tasso–Olver equations

Cited by 15 publications

References 53 publications

Parametric quintic spline for time fractional Burger’s and coupled Burgers’ equations

Parametric quintic spline for time fractional Burger’s and coupled Burgers’ equations

Numerical solutions of time and space fractional coupled Burgers equations using time–space Chebyshev pseudospectral method

Efficient numerical schemes for the solution of generalized time fractional Burgers type equations

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