scholarly journals New Implementation of Residual Power Series for Solving Fuzzy Fractional Riccati Equation

2018 ◽  
Vol 10 (2) ◽  
pp. 81
Author(s):  
Moath Ali Alshorman ◽  
Nurnadiah Zamri ◽  
Mohammed Ali ◽  
Asia Khalaf Albzeirat
Keyword(s):  
Power Series ◽  
Riccati Equation ◽  
Fractional Power ◽  
High Accuracy ◽  
Computational Method ◽  
Power Series Method ◽  
Residual Power Series Method ◽  
Residual Power Series ◽  
Fractional Power Series ◽  
Residual Power

This paper reveals a computational method using a Residual Power Series Method (RPSM) for the solution of fuzzy fractional riccati equation under caputo fractional differentiability. An analytical solution of fuzzy fractional riccati equation is obtained as a convergent fractional power series. The procedure produces solutions of high accuracy, and some illustrative examples are solved with a different value of orders to show the efficiency of the RPSM.

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.

scholarly journals Analytical Solution of the Fractional Fredholm Integrodifferential Equation Using the Fractional Residual Power Series Method

Complexity ◽  
2017 ◽  
Vol 2017 ◽  
pp. 1-6 ◽  
Author(s):  
Muhammed I. Syam
Keyword(s):  
Power Series ◽  
Integrodifferential Equation ◽  
Fractional Power ◽  
Series Method ◽  
Power Series Method ◽  
Residual Power Series Method ◽  
Residual Functions ◽  
Residual Power Series ◽  
Fractional Power Series ◽  
Residual Power

We study the solution of fractional Fredholm integrodifferential equation. A modified version of the fractional power series method (RPS) is presented to extract an approximate solution of the model. The RPS method is a combination of the generalized fractional Taylor series and the residual functions. To show the efficiency of the proposed method, numerical results are presented.

scholarly journals Toward computational algorithm for time-fractional Fokker–Planck models

2019 ◽  
Vol 11 (10) ◽  
pp. 168781401988103 ◽  
Author(s):  
Asad Freihet ◽  
Shatha Hasan ◽  
Mohammad Alaroud ◽  
Mohammed Al-Smadi ◽  
Rokiah Rozita Ahmad ◽  
...  
Keyword(s):  
Power Series ◽  
Differential Equations ◽  
Fractional Power ◽  
Series Method ◽  
Power Series Method ◽  
Residual Power Series Method ◽  
Wide Range ◽  
Residual Power Series ◽  
Residual Power ◽  
Fokker Planck

This article describes an efficient algorithm based on residual power series to approximate the solution of a class of partial differential equations of time-fractional Fokker–Planck model. The fractional derivative is assumed in the Caputo sense. The proposed algorithm gives the solution in a form of rapidly convergent fractional power series with easily computable coefficients. It does not require linearization, discretization, or small perturbation. To test simplicity, potentiality, and practical usefulness of the proposed algorithm, illustrative examples are provided. The approximate solutions of time-fractional Fokker–Planck equations are obtained by the residual power series method are compared with those obtained by other existing methods. The present results and graphics reveal the ability of residual power series method to deal with a wide range of partial fractional differential equations emerging in the modeling of physical phenomena of science and engineering.

scholarly journals Solving Boundary-Layer Problems by Residual-Power-Series Method

2016 ◽  
Vol 8 (3) ◽  
pp. 68
Author(s):  
Mohd Taib Shatnawi
Keyword(s):  
Boundary Layer ◽  
Power Series ◽  
Nonlinear Boundary ◽  
Power Series Method ◽  
Boundary Layer Equations ◽  
Residual Power Series Method ◽  
Residual Power Series ◽  
Linear And Nonlinear ◽  
Boundary Layer Problems ◽  
Residual Power

<p><span lang="EN-US">In this paper, the so-called residual-power-series (RPS) method is presented for solving nonlinear boundary-layer equations. The RPS method provides a single unified treatment for the linear and nonlinear terms in the equations. The accuracy and efficiency of the RPS method is demonstrated for both a single and a system of two coupled boundary-layer equations on an unbounded domain.</span></p>

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