scholarly journals Local Fractional Laplace Variational Iteration Method for Solving Linear Partial Differential Equations with Local Fractional Derivative

2014 ◽  
Vol 2014 ◽  
pp. 1-8 ◽  
Author(s):  
Ai-Min Yang ◽  
Jie Li ◽  
H. M. Srivastava ◽  
Gong-Nan Xie ◽  
Xiao-Jun Yang
Keyword(s):  
Partial Differential Equations ◽  
Differential Equations ◽  
Fractional Derivative ◽  
Iteration Method ◽  
Variational Iteration Method ◽  
Approximate Solutions ◽  
Fractional Partial Differential Equations ◽  
Partial Differential ◽  
Variational Iteration ◽  
Linear Partial Differential Equations

The local fractional Laplace variational iteration method was applied to solve the linear local fractional partial differential equations. The local fractional Laplace variational iteration method is coupled by the local fractional variational iteration method and Laplace transform. The nondifferentiable approximate solutions are obtained and their graphs are also shown.

scholarly journals Solitary and compacton solutions of fractional KdV-like equations

Open Physics ◽  
2016 ◽  
Vol 14 (1) ◽  
pp. 328-336 ◽  
Author(s):  
Bo Tang ◽  
Yingzhe Fan ◽  
Jianping Zhao ◽  
Xuemin Wang
Keyword(s):  
Partial Differential Equations ◽  
Differential Equations ◽  
Iteration Method ◽  
Variational Iteration Method ◽  
Fractional Partial Differential Equations ◽  
Partial Differential ◽  
Reliable Tool ◽  
Variational Iteration ◽  
He’S Polynomials ◽  
Liouville Derivative

AbstractIn this paper, based on Jumarie’s modified Riemann-Liouville derivative, we apply the fractional variational iteration method using He’s polynomials to obtain solitary and compacton solutions of fractional KdV-like equations. The results show that the proposed method provides a very effective and reliable tool for solving fractional KdV-like equations, and the method can also be extended to many other fractional partial differential equations.

scholarly journals Convergence of Variational Iteration Method for Solving Singular Partial Differential Equations of Fractional Order

2014 ◽  
Vol 2014 ◽  
pp. 1-11
Author(s):  
Asma Ali Elbeleze ◽  
Adem Kılıçman ◽  
Bachok M. Taib
Keyword(s):  
Partial Differential Equations ◽  
Differential Equations ◽  
Fractional Order ◽  
Iteration Method ◽  
Series Solution ◽  
Fractional Derivatives ◽  
Variational Iteration Method ◽  
Approximate Solutions ◽  
Partial Differential ◽  
Variational Iteration

We are concerned here with singular partial differential equations of fractional order (FSPDEs). The variational iteration method (VIM) is applied to obtain approximate solutions of this type of equations. Convergence analysis of the VIM is discussed. This analysis is used to estimate the maximum absolute truncated error of the series solution. A comparison between the results of VIM solutions and exact solution is given. The fractional derivatives are described in Caputo sense.

scholarly journals Couple of the Variational Iteration Method and Legendre Wavelets for Nonlinear Partial Differential Equations

2013 ◽  
Vol 2013 ◽  
pp. 1-11 ◽  
Author(s):  
Fukang Yin ◽  
Junqiang Song ◽  
Xiaoqun Cao ◽  
Fengshun Lu
Keyword(s):  
Partial Differential Equations ◽  
Differential Equations ◽  
Iteration Method ◽  
Nonlinear Partial Differential Equations ◽  
Variational Iteration Method ◽  
Approximate Solutions ◽  
Legendre Wavelets ◽  
Partial Differential ◽  
Variational Iteration ◽  
Block Pulse Functions

This paper develops a modified variational iteration method coupled with the Legendre wavelets, which can be used for the efficient numerical solution of nonlinear partial differential equations (PDEs). The approximate solutions of PDEs are calculated in the form of a series whose components are computed by applying a recursive relation. Block pulse functions are used to calculate the Legendre wavelets coefficient matrices of the nonlinear terms. The main advantage of the new method is that it can avoid solving the nonlinear algebraic system and symbolic computation. Furthermore, the developed vector-matrix form makes it computationally efficient. The results show that the proposed method is very effective and easy to implement.

scholarly journals Fractional Variational Iteration Method for Solving Fractional Partial Differential Equations with Proportional Delay

2017 ◽  
Vol 2017 ◽  
pp. 1-11 ◽  
Author(s):  
Brajesh Kumar Singh ◽  
Pramod Kumar
Keyword(s):  
Partial Differential Equations ◽  
Differential Equations ◽  
Iteration Method ◽  
Variational Iteration Method ◽  
Physical Models ◽  
Proportional Delay ◽  
Approximate Analytic Solution ◽  
Fractional Partial Differential Equations ◽  
Partial Differential ◽  
Variational Iteration

This paper deals with an alternative approximate analytic solution to time fractional partial differential equations (TFPDEs) with proportional delay, obtained by using fractional variational iteration method, where the fractional derivative is taken in Caputo sense. The proposed series solutions are found to converge to exact solution rapidly. To confirm the efficiency and validity of FRDTM, the computation of three test problems of TFPDEs with proportional delay was presented. The scheme seems to be very reliable, effective, and efficient powerful technique for solving various types of physical models arising in science and engineering.

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