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 Adomian Decomposition and Fractional Power Series Solution of a Class of Nonlinear Fractional Differential Equations

Mathematics ◽  
2021 ◽  
Vol 9 (9) ◽  
pp. 1070
Author(s):  
Pshtiwan Othman Mohammed ◽  
José António Tenreiro Machado ◽  
Juan L. G. Guirao ◽  
Ravi P. Agarwal
Keyword(s):  
Power Series ◽  
Differential Equations ◽  
Fractional Differential Equations ◽  
Fractional Power ◽  
Power Series Solution ◽  
True Nature ◽  
Nonlinear Fractional Differential Equations ◽  
Adomian Decomposition ◽  
Fractional Differential ◽  
Fractional Power Series

Nonlinear fractional differential equations reflect the true nature of physical and biological models with non-locality and memory effects. This paper considers nonlinear fractional differential equations with unknown analytical solutions. The Adomian decomposition and the fractional power series methods are adopted to approximate the solutions. The two approaches are illustrated and compared by means of four numerical examples.

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 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 FRACTIONAL POWER SERIES APPROACH FOR THE SOLUTION OF FRACTIONAL-ORDER INTEGRO-DIFFERENTIAL EQUATIONS

Fractals ◽  
2021 ◽  
Author(s):  
MUHAMMAD AKBAR ◽  
RASHID NAWAZ ◽  
SUMBAL AHSAN ◽  
KOTTAKKARAN SOOPPY NISAR ◽  
KAMAL SHAH ◽  
...  
Keyword(s):  
Power Series ◽  
Differential Equations ◽  
Fractional Power ◽  
Power Series Method ◽  
Transform Method ◽  
Residual Power Series ◽  
Fractional Differential ◽  
Optimal Homotopy Asymptotic Method ◽  
Trigonometric Transform ◽  
Fractional Power Series

Fractional differential and integral equations are focus of the researchers owing to their tremendous applications in different field of science and technology, such as physics, chemistry, mathematical biology, dynamical system and engineering. In this work, a power series approach called Residual Power Series Method (RPSM) is applied for the solution of fractional (non-integer) order integro-differential equations (FIDEs). The Caputo sense is used for calculating fractional derivatives. Comparison of the obtained solution is made with the Trigonometric Transform Method (TTM) and Optimal Homotopy Asymptotic Method (OHAM). There is no restrictive condition on the proposed solution. The presented technique is simple in applicability and easily computable.

scholarly journals Computational Optimization of Residual Power Series Algorithm for Certain Classes of Fuzzy Fractional Differential Equations

2018 ◽  
Vol 2018 ◽  
pp. 1-11 ◽  
Author(s):  
Mohammad Alaroud ◽  
Mohammed Al-Smadi ◽  
Rokiah Rozita Ahmad ◽  
Ummul Khair Salma Din
Keyword(s):  
Power Series ◽  
Differential Equations ◽  
Fractional Differential Equations ◽  
Optimization Technique ◽  
Fractional Power ◽  
Taylor Formula ◽  
Residual Power Series ◽  
Fractional Differential ◽  
Residual Power ◽  
Fuzzy Fractional Differential Equations

This paper aims to present a novel optimization technique, the residual power series (RPS), for handling certain classes of fuzzy fractional differential equations of order 1<γ≤2 under strongly generalized differentiability. The proposed technique relies on generalized Taylor formula under Caputo sense aiming at extracting a supportive analytical solution in convergent series form. The RPS algorithm is significant and straightforward tool for creating a fractional power series solution without linearization, limitation on the problem’s nature, sort of classification, or perturbation. Some illustrative examples are provided to demonstrate the feasibility of the RPS scheme. The results obtained show that the scheme is simple and reliable and there is good agreement with exact solution.

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.

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