scholarly journals A non-differentiable solution for the local fractional telegraph equation

2017 ◽  
Vol 21 (suppl. 1) ◽  
pp. 225-231
Author(s):  
Jie Li ◽  
Ce Zhang ◽  
Weixing Liu ◽  
Yuzhu Zhang ◽  
Aimin Yang ◽  
...  
Keyword(s):  
Analytical Solution ◽  
Fractional Derivative ◽  
Series Expansion ◽  
Expansion Method ◽  
Telegraph Equation ◽  
Differentiable Solution ◽  
Local Fractional Derivative ◽  
Fractional Telegraph Equation ◽  
Telegraph Equations ◽  
Series Expansion Method

In this paper, we consider the linear telegraph equations with local fractional derivative. The local fractional Laplace series expansion method is used to handle the local fractional telegraph equation. The analytical solution with the non-differentiable graphs is discussed in detail. The proposed method is efficient and accurate.

scholarly journals Approximation Solutions for Local Fractional Schrödinger Equation in the One-Dimensional Cantorian System

2013 ◽  
Vol 2013 ◽  
pp. 1-5 ◽  
Author(s):  
Yang Zhao ◽  
De-Fu Cheng ◽  
Xiao-Jun Yang
Keyword(s):  
Fractional Derivative ◽  
Series Expansion ◽  
Present Method ◽  
Expansion Method ◽  
One Dimensional ◽  
Local Fractional Derivative ◽  
Simple Tool ◽  
Fractional Schrödinger Equations ◽  
The One ◽  
Series Expansion Method

The local fractional Schrödinger equations in the one-dimensional Cantorian system are investigated. The approximations solutions are obtained by using the local fractional series expansion method. The obtained solutions show that the present method is an efficient and simple tool for solving the linear partial differentiable equations within the local fractional derivative.

scholarly journals Application of the Local Fractional Series Expansion Method and the Variational Iteration Method to the Helmholtz Equation Involving Local Fractional Derivative Operators

2013 ◽  
Vol 2013 ◽  
pp. 1-6 ◽  
Author(s):  
Ai-Min Yang ◽  
Zeng-Shun Chen ◽  
H. M. Srivastava ◽  
Xiao-Jun Yang
Keyword(s):  
Fractional Derivative ◽  
Helmholtz Equation ◽  
Series Expansion ◽  
Iteration Method ◽  
Variational Iteration Method ◽  
Expansion Method ◽  
Local Fractional Derivative ◽  
Variational Iteration ◽  
Fractional Derivative Operators ◽  
Series Expansion Method

We investigate solutions of the Helmholtz equation involving local fractional derivative operators. We make use of the series expansion method and the variational iteration method, which are based upon the local fractional derivative operators. The nondifferentiable solution of the problem is obtained by using these methods.

scholarly journals Introduction of the Phone-Concept Into Pole Figure Inversion Using the Iterative Series Expansion Method

1992 ◽  
Vol 19 (3) ◽  
pp. 169-174 ◽  
Author(s):  
M. Dahms
Keyword(s):  
Texture Analysis ◽  
Pole Figure ◽  
Series Expansion ◽  
Expansion Method ◽  
Probabilistic Methods ◽  
Series Expansion Method

The phone-concept as it is used in the various kinds of probabilistic methods can easily be applied to the iterative series expansion method for quantitative texture analysis. Only slight modifications of the existing routines are necessary. The advantages of this concept are demonstrated by a mathematical and an experimental example.

scholarly journals COMPARISON OF A GENERAL SERIES EXPANSION METHOD AND THE HOMOTOPY ANALYSIS METHOD

2010 ◽  
Vol 24 (15) ◽  
pp. 1699-1706 ◽  
Author(s):  
CHENG-SHI LIU ◽  
YANG LIU
Keyword(s):  
Series Expansion ◽  
Homotopy Analysis Method ◽  
Nonlinear Differential Equations ◽  
Expansion Method ◽  
Basis Functions ◽  
Analysis Method ◽  
Convergence Region ◽  
General Series ◽  
Homotopy Analysis ◽  
Series Expansion Method

A simple analytic tool, namely the general series expansion method, is proposed to find the solutions for nonlinear differential equations. A set of suitable basis functions [Formula: see text] is chosen such that the solution to the equation can be expressed by [Formula: see text]. In general, t0 can control and adjust the convergence region of the series solution such that our method has the same effect as the homotopy analysis method proposed by Liao, but our method is simpler and clearer. As a result, we show that the secret parameter h in the homotopy analysis methods can be explained by using our parameter t0. Therefore, our method reveals a key secret in the homotopy analysis method. For the purpose of comparison with the homotopy analysis method, a typical example is studied in detail.

Series Expansion Method

2015 ◽  
pp. 63-83
Author(s):  
Matthew N. O. Sadiku ◽  
Sudarshan R. Nelatury
Keyword(s):  
Series Expansion ◽  
Expansion Method ◽  
Series Expansion Method
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