Residual power series method for fractional Burger types equations

AbstractWe present an analytic algorithm to solve the generalized Berger-Fisher (B-F) equation, B-F equation, generalized Fisher equation and Fisher equation by using residual power series method (RPSM), which is based on the generalized Taylor’s series formula together with the residual error function. In all the cases obtained results are verified through the different graphical representation. Comparison of the results obtained by the present method with exact solution reveals that the accuracy and fast convergence of the proposed method.

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A new iterative algorithm on the time-fractional Fisher equation: Residual power series method

Advances in Mechanical Engineering ◽

10.1177/1687814017716009 ◽

2017 ◽

Vol 9 (9) ◽

pp. 168781401771600 ◽

Cited By ~ 7

Author(s):

Maysaa’ Mohamed Al Qurashi ◽

Zeliha Korpinar ◽

Dumitru Baleanu ◽

Mustafa Inc

Keyword(s):

Power Series ◽

Iterative Algorithm ◽

Fisher Equation ◽

Series Method ◽

Power Series Method ◽

Residual Power Series Method ◽

Residual Power Series ◽

Residual Power

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An Approximate Solution of the Time-Fractional Fisher Equation with Small Delay by Residual Power Series Method

Mathematical Problems in Engineering ◽

10.1155/2018/9471910 ◽

2018 ◽

Vol 2018 ◽

pp. 1-8 ◽

Cited By ~ 1

Author(s):

Ali Demir ◽

Mine Aylin Bayrak ◽

Ebru Ozbilge

Keyword(s):

Analytical Solution ◽

Power Series ◽

Fisher Equation ◽

Series Method ◽

Power Series Method ◽

Delay Term ◽

Residual Power Series Method ◽

Small Delay ◽

Residual Power Series ◽

Residual Power

An analytical solution of the time-fractional Fisher equation with small delay is established by means of residual the residual power series method (RPSM) where the fractional derivative is taken in the Caputo sense. Taking advantage of small delay, the time-fractional Fisher equation is expanded in powers series of delay term ϵ. By using RPSM analytical solution of time-fractional of Fisher equation is constructed. The final results and graphical consequences illustrate that the proposed method in this study is very efficient, effective, and reliable for the solution of the time-fractional Fisher equation with small delay.

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Analytical Solution for the Time Fractional BBM-Burger Equation by Using Modified Residual Power Series Method

Complexity ◽

10.1155/2018/2891373 ◽

2018 ◽

Vol 2018 ◽

pp. 1-11 ◽

Cited By ~ 1

Author(s):

Jianke Zhang ◽

Zhirou Wei ◽

Longquan Yong ◽

Yuelei Xiao

Keyword(s):

Power Series ◽

Burger Equation ◽

Numerical Solutions ◽

Error Function ◽

Series Method ◽

Power Series Method ◽

Transform Method ◽

Residual Power Series Method ◽

Residual Power Series ◽

Residual Power

In this study, a generalized Taylor series formula together with residual error function, which is named the residual power series method (RPSM), is used for finding the series solution of the time fractional Benjamin-Bona-Mahony-Burger (BBM-Burger) equation. The BBM-Burger equation is useful in describing approximately the unidirectional propagation of long waves in certain nonlinear dispersive systems. The numerical solution of the BBM-Burger equation is calculated by Maple. The numerical results show that the RPSM is reliable and powerful in solving the numerical solutions of the BBM-Burger equation compared with the exact solutions as well as the solutions obtained by homotopy analysis transform method through different graphical representations and tables.

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