scholarly journals A numerical method for solving singular Riccati equation with fractional order by modified fractional power series method

2018 ◽  
Vol 2018 (2) ◽  
pp. 100-110
Author(s):  
Muhammed I. Syam ◽  
Marwa Al Refai ◽  
Asia Alneyadi ◽  
Alaa Haroun ◽  
Khatema Al Braiki
Keyword(s):  
Power Series ◽  
Numerical Method ◽  
Riccati Equation ◽  
Fractional Order ◽  
Fractional Power ◽  
Series Method ◽  
Power Series Method ◽  
Fractional Power Series

scholarly journals Method for Evaluating Fractional Derivatives of Fractional Functions

2020 ◽  
pp. 286-290
Author(s):  
Chii-Huei Yu
Keyword(s):  
Power Series ◽  
Fractional Derivatives ◽  
Fractional Power ◽  
Series Method ◽  
Power Series Method ◽  
Differential Problem ◽  
Fractional Differential ◽  
Derivatives Of ◽  
Fractional Power Series

This paper studies the fractional differential problem of fractional functions, regarding the modified Riemann-Liouvellie (R-L) fractional derivatives. A new multiplication and the fractional power series method are used to obtain any order fractional derivatives of some elementary fractional functions.

scholarly journals An algorithm for solving fractional Zakharov-Kuznetsv equations

2016 ◽  
Vol 12 (7) ◽  
pp. 6398-6401
Author(s):  
Huijuan Jia
Keyword(s):  
Power Series ◽  
Computer Program ◽  
Fractional Power ◽  
The Other ◽  
Series Method ◽  
Power Series Method ◽  
Fractional Power Series

By using the fractional power series method, we give an algorithm for solving fractional Zakharov-Kuznetsv equations . Compared to the other method, the fractional power series method is more derect , effective and the algorithm can be implemented as a computer program.

scholarly journals An analytical solution for a fractional heat-like equation with variable coefficients

2017 ◽  
Vol 21 (4) ◽  
pp. 1759-1764 ◽  
Author(s):  
Run-qing Cui ◽  
Tao Ban
Keyword(s):  
Analytical Solution ◽  
Power Series ◽  
Solution Process ◽  
Fractional Power ◽  
Variable Coefficients ◽  
Series Method ◽  
Power Series Method ◽  
Fractional Power Series

The fractional power series method is used to solve a fractional heat-like equations with variable coefficients. The solution process is elucidated, and the results show that the method is simple but effective.

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 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 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.

scholarly journals The fractional power series method an efficient candidate for solving fractional systems

2018 ◽  
Vol 22 (4) ◽  
pp. 1745-1751 ◽  
Author(s):  
Feng Ren ◽  
Yue Hu
Keyword(s):  
Power Series ◽  
Solution Process ◽  
Fractional Power ◽  
Initial Solution ◽  
Great Success ◽  
Series Method ◽  
Power Series Method ◽  
Fractional Systems ◽  
Fractional Differential ◽  
Fractional Power Series

The fractional power series method was originally proposed to solve a fractional differential equation. This paper extends the method to a system of fractional differential equations with great success. How to construct an initial solution, plays an important role in the solution process and an example is given to elucidate the choice of the initial solution.

scholarly journals Approximate analytic solution for multi-dimensional fractional wave-like equation

2020 ◽  
Vol 24 (4) ◽  
pp. 2645-2652
Author(s):  
Jian-She Sun
Keyword(s):  
Power Series ◽  
Fractional Derivatives ◽  
Analytic Solution ◽  
Fractional Power ◽  
Variable Coefficients ◽  
Approximate Analytic Solution ◽  
Series Method ◽  
Power Series Method ◽  
Fractional Power Series

The fractional power series method is used to solve 2- and 3-D fractional wave-like models with variable coefficients. The fractional derivatives are described in the Caputo sense. Two examples are considered to show the effectiveness and convenience of the method.

scholarly journals A Truncation Method for Solving the Time-Fractional Benjamin-Ono Equation

2019 ◽  
Vol 2019 ◽  
pp. 1-7 ◽  
Author(s):  
Mohamed R. Ali
Keyword(s):  
Differential Equation ◽  
Ordinary Differential Equation ◽  
Power Series ◽  
Fractional Order ◽  
Nonlinear Ordinary Differential Equation ◽  
Lie Symmetry ◽  
Series Method ◽  
Lie Symmetry Analysis ◽  
Power Series Method ◽  
Bo Equation

We deem the time-fractional Benjamin-Ono (BO) equation out of the Riemann–Liouville (RL) derivative by applying the Lie symmetry analysis (LSA). By first using prolongation theorem to investigate its similarity vectors and then using these generators to transform the time-fractional BO equation to a nonlinear ordinary differential equation (NLODE) of fractional order, we complete the solutions by utilizing the power series method (PSM).

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