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

2017 ◽  
Vol 9 (9) ◽  
pp. 168781401771600 ◽  
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

Residual power series method for fractional Burger types equations

2016 ◽  
Vol 5 (4) ◽  
Author(s):  
Amit Kumar ◽  
Sunil Kumar
Keyword(s):  
Power Series ◽  
Graphical Representation ◽  
Error Function ◽  
Fisher Equation ◽  
Series Method ◽  
Power Series Method ◽  
Residual Power Series Method ◽  
Residual Power Series ◽  
Comparison Of The Results ◽  
Residual Power

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.

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

2018 ◽  
Vol 2018 ◽  
pp. 1-8 ◽  
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.

scholarly journals Solutions of the time fractional reaction–diffusion equations with residual power series method

2016 ◽  
Vol 8 (10) ◽  
pp. 168781401667086 ◽  
Author(s):  
Fairouz Tchier ◽  
Mustafa Inc ◽  
Zeliha S Korpinar ◽  
Dumitru Baleanu
Keyword(s):  
Power Series ◽  
Reaction Diffusion ◽  
Reaction Diffusion Equations ◽  
Diffusion Equations ◽  
Series Method ◽  
Power Series Method ◽  
Residual Power Series Method ◽  
Residual Power Series ◽  
Residual Power ◽  
Fractional Reaction

Solution of Fractional SIR Epidemic Model Using Residual Power Series Method

2019 ◽  
Vol 13 (2) ◽  
pp. 153-161 ◽  
Author(s):  
Shatha Hasan ◽  
Ayat Al-Zoubi ◽  
Asad Freihet ◽  
Mohammed Al-Smad ◽  
Shaher Momani
Keyword(s):  
Power Series ◽  
Epidemic Model ◽  
Series Method ◽  
Sir Epidemic Model ◽  
Power Series Method ◽  
Residual Power Series Method ◽  
Sir Epidemic ◽  
Residual Power Series ◽  
Residual Power

scholarly journals Asymptotic Solutions of Time-Space Fractional Coupled Systems by Residual Power Series Method

2017 ◽  
Vol 2017 ◽  
pp. 1-10 ◽  
Author(s):  
Wenjin Li ◽  
Yanni Pang
Keyword(s):  
Power Series ◽  
Fractional Derivative ◽  
Coupled Systems ◽  
Asymptotic Solutions ◽  
Series Method ◽  
Power Series Method ◽  
Residual Power Series Method ◽  
Time Space ◽  
Residual Power Series ◽  
Residual Power

This paper focuses on the asymptotic solutions to time-space fractional coupled systems, where the fractional derivative and integral are described in the sense of Caputo derivative and Riemann-Liouville integral. We introduce the Residual Power Series (for short RPS) method to construct the desired asymptotic solutions. Furthermore, we apply this method to some time-space fractional coupled systems. The simplicity and efficiency of RPS method are shown by the application.

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