scholarly journals Local Fractional Series Expansion Method for Solving Wave and Diffusion Equations on Cantor Sets

2013 ◽  
Vol 2013 ◽  
pp. 1-5 ◽  
Author(s):  
Ai-Min Yang ◽  
Xiao-Jun Yang ◽  
Zheng-Biao Li
Keyword(s):  
Differential Equations ◽  
Series Expansion ◽  
Analytical Solutions ◽  
Fractional Derivatives ◽  
Expansion Method ◽  
Cantor Sets ◽  
Diffusion Equations ◽  
And Diffusion ◽  
Series Expansion Method

We proposed a local fractional series expansion method to solve the wave and diffusion equations on Cantor sets. Some examples are given to illustrate the efficiency and accuracy of the proposed method to obtain analytical solutions to differential equations within the local fractional derivatives.

scholarly journals Application of Local Fractional Series Expansion Method to Solve Klein-Gordon Equations on Cantor Sets

2014 ◽  
Vol 2014 ◽  
pp. 1-6 ◽  
Author(s):  
Ai-Min Yang ◽  
Yu-Zhu Zhang ◽  
Carlo Cattani ◽  
Gong-Nan Xie ◽  
Mohammad Mehdi Rashidi ◽  
...  
Keyword(s):  
Differential Equations ◽  
Series Expansion ◽  
Analytical Solutions ◽  
Fractional Derivatives ◽  
Expansion Method ◽  
Cantor Sets ◽  
Present Technique ◽  
Klein Gordon ◽  
Series Expansion Method

We use the local fractional series expansion method to solve the Klein-Gordon equations on Cantor sets within the local fractional derivatives. The analytical solutions within the nondifferential terms are discussed. The obtained results show the simplicity and efficiency of the present technique with application to the problems of the liner differential equations on Cantor sets.

scholarly journals Laplace transform series expansion method for solving the local fractional heat-transfer equation defined on Cantor sets

2016 ◽  
Vol 20 (suppl. 3) ◽  
pp. 777-780
Author(s):  
Huan Sun ◽  
Xing-Hua Liu
Keyword(s):  
Heat Transfer ◽  
Laplace Transform ◽  
Series Expansion ◽  
Transfer Equation ◽  
Expansion Method ◽  
Cantor Sets ◽  
Heat Transfer Equation ◽  
Local Fractional Calculus ◽  
The Laplace Transform ◽  
Series Expansion Method

In this paper, we use the Laplace transform series expansion method to find the analytical solution for the local fractional heat-transfer equation defined on Cantor sets via local fractional calculus.

Fractional series expansion method for fractional differential equations

2015 ◽  
Vol 25 (7) ◽  
pp. 1525-1530 ◽  
Author(s):  
Zheng-Biao Li ◽  
Wei-Hong Zhu
Keyword(s):  
Differential Equations ◽  
Series Expansion ◽  
Fractional Differential Equations ◽  
Expansion Method ◽  
Kantorovich Method ◽  
Content Type ◽  
Analytical Technique ◽  
Liouville Derivative ◽  
Fractional Differential ◽  
Series Expansion Method

Purpose – The purpose of this paper is to suggest a new analytical technique called the fractional series expansion method for solving linear fractional differential equations (FDEs). Design/methodology/approach – This method is based on the idea of Kantorovich method, convergent series, and the modified Riemann-Liouville derivative. Findings – This work suggests a new analytical technique. The FDEs are described in Jumarie’s sense. Originality/value – It finds a new method for solving linear FDEs. The solution procedure is elucidated by two examples.

Application of the exp(-φ)-expansion method to the Pochhammer-Chree equation

Filomat ◽  
2018 ◽  
Vol 32 (9) ◽  
pp. 3347-3354 ◽  
Author(s):  
Nematollah Kadkhoda ◽  
Michal Feckan ◽  
Yasser Khalili
Keyword(s):  
Partial Differential Equations ◽  
Differential Equations ◽  
Exact Solutions ◽  
Present Article ◽  
Analytical Solutions ◽  
Nonlinear Differential Equations ◽  
Nonlinear Partial Differential Equations ◽  
Rational Functions ◽  
Expansion Method ◽  
Exponential Functions

In the present article, a direct approach, namely exp(-?)-expansion method, is used for obtaining analytical solutions of the Pochhammer-Chree equations which have a many of models. These solutions are expressed in exponential functions expressed by hyperbolic, trigonometric and rational functions with some parameters. Recently, many methods were attempted to find exact solutions of nonlinear partial differential equations, but it seems that the exp(-?)-expansion method appears to be efficient for finding exact solutions of many nonlinear differential equations.

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