scholarly journals The Laplace series solution for local fractional Korteweg-de Vries equation

2016 ◽  
Vol 20 (suppl. 3) ◽  
pp. 867-870 ◽  
Author(s):  
Shan-Shan Ye ◽  
Syed Mohyud-Din ◽  
Fethi Belgacem

In this paper, we consider a new application of the local fractional Laplace series expansion method to handle the local fractional Korteweg-de Vries equation. The obtained solution with non-differentiable type shows that the technology is accurate and efficient.

2016 ◽  
Vol 20 (suppl. 3) ◽  
pp. 863-866
Author(s):  
Wei Zhang ◽  
Kai-Li Xu ◽  
Yun Lei

In this paper, the local fractional series expansion method is used to find the series solution for the local fractional Korteweg-de Vries equation.


1992 ◽  
Vol 19 (3) ◽  
pp. 169-174 ◽  
Author(s):  
M. Dahms

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.


2010 ◽  
Vol 24 (15) ◽  
pp. 1699-1706 ◽  
Author(s):  
CHENG-SHI LIU ◽  
YANG LIU

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.


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

2016 ◽  
Vol 20 (suppl. 3) ◽  
pp. 777-780
Author(s):  
Huan Sun ◽  
Xing-Hua Liu

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.


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