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.

scholarly journals Construction of Fractional Power Series Solutions to Fractional Boussinesq Equations Using Residual Power Series Method

2016 ◽  
Vol 2016 ◽  
pp. 1-15 ◽  
Author(s):  
Fei Xu ◽  
Yixian Gao ◽  
Xue Yang ◽  
He Zhang
Keyword(s):  
Power Series ◽  
Fractional Power ◽  
Boussinesq Equations ◽  
Power Series Method ◽  
Residual Power Series Method ◽  
Time Space ◽  
Residual Power Series ◽  
Fractional Differential ◽  
Fractional Power Series ◽  
Residual Power

This paper is aimed at constructing fractional power series (FPS) solutions of time-space fractional Boussinesq equations using residual power series method (RPSM). Firstly we generalize the idea of RPSM to solve any-order time-space fractional differential equations in high-dimensional space with initial value problems inRn. Using RPSM, we can obtain FPS solutions of fourth-, sixth-, and 2nth-order time-space fractional Boussinesq equations inRand fourth-order time-space fractional Boussinesq equations inR2andRn. Finally, by numerical experiments, it is shown that RPSM is a simple, effective, and powerful method for seeking approximate analytic solutions of fractional differential equations.

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 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
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