scholarly journals Attractive new fractional-integer power series method for solving singularly perturbed differential equations involving mixed fractional and integer derivatives

2021 ◽  
Vol 20 ◽  
pp. 103780
Author(s):  
Issam Abu Irwaq ◽  
Marwan Alquran ◽  
Mohammed Ali ◽  
Imad Jaradat ◽  
M.S.M. Noorani
Keyword(s):  
Power Series ◽  
Differential Equations ◽  
Singularly Perturbed ◽  
Series Method ◽  
Power Series Method ◽  
Integer Power

scholarly journals Applications of General Residual Power Series Method to Differential Equations with Variable Coefficients

2018 ◽  
Vol 2018 ◽  
pp. 1-9 ◽  
Author(s):  
Bochao Chen ◽  
Li Qin ◽  
Fei Xu ◽  
Jian Zu
Keyword(s):  
Power Series ◽  
Differential Equations ◽  
Variable Coefficients ◽  
Series Solutions ◽  
Series Method ◽  
Power Series Method ◽  
Residual Power Series Method ◽  
Residual Power Series ◽  
Analytical Series ◽  
Residual Power

This paper is devoted to studying the analytical series solutions for the differential equations with variable coefficients. By a general residual power series method, we construct the approximate analytical series solutions for differential equations with variable coefficients, including nonhomogeneous parabolic equations, fractional heat equations in 2D, and fractional wave equations in 3D. These applications show that residual power series method is a simple, effective, and powerful method for seeking analytical series solutions of differential equations (especially for fractional differential equations) with variable coefficients.

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 Fractional power series method for solving fractional differemtial equation

2016 ◽  
Vol 12 (4) ◽  
pp. 6156-6159 ◽  
Author(s):  
Runqing Cui ◽  
Yue Hu
Keyword(s):  
Power Series ◽  
Differential Equations ◽  
Fractional Differential Equations ◽  
Fractional Power ◽  
The Other ◽  
Series Method ◽  
Power Series Method ◽  
Nonlinear Fractional Differential Equations ◽  
Fractional Differential ◽  
Fractional Power Series

we use fractional power series method (FPSM) to solve some linear or nonlinear fractional differential equations . Compared to the other method, the FPSM is more simple, derect and effective.

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