scholarly journals Variational Iteration Transform Method for Fractional Differential Equations with Local Fractional Derivative

2014 ◽  
Vol 2014 ◽  
pp. 1-9 ◽  
Author(s):  
Yong-Ju Yang ◽  
Liu-Qing Hua
Keyword(s):  
Fractional Derivative ◽  
Fractional Differential Equations ◽  
Iteration Method ◽  
Variational Iteration Method ◽  
Transform Method ◽  
Local Fractional Derivative ◽  
Variational Iteration ◽  
Differential Transform ◽  
Differential Operation ◽  
Fractional Differential

We propose the variational iteration transform method in the sense of local fractional derivative, which is derived from the coupling method of local fractional variational iteration method and differential transform method. The method reduces the integral calculation of the usual variational iteration computations to more easily handled differential operation. And the technique is more orderly and easier to analyze computing result as compared with the local fractional variational iteration method. Some examples are illustrated to show the feature of the presented technique.

scholarly journals A new method solving local fractional differential equations in heat transfer

2019 ◽  
Vol 23 (3 Part A) ◽  
pp. 1663-1669
Author(s):  
Yong-Ju Yang
Keyword(s):  
Heat Transfer ◽  
Differential Equations ◽  
Fractional Differential Equations ◽  
Differential Transform Method ◽  
New Method ◽  
Transform Method ◽  
Variational Iteration ◽  
Differential Transform ◽  
Differential Operation ◽  
Fractional Differential

In this article, a new method, which is coupled by the variational iteration and reduced differential transform method, is proposed to solve local fractional differential equations. The advantage of the method is that the integral operation of variational iteration is transformed into the differential operation. One test examples is presented to demonstrate the reliability and efficiency of the proposed method.

scholarly journals Variational Iteration Method for a Fractional-Order Brusselator System

2014 ◽  
Vol 2014 ◽  
pp. 1-6 ◽  
Author(s):  
H. Jafari ◽  
Abdelouahab Kadem ◽  
D. Baleanu
Keyword(s):  
Fractional Order ◽  
Fractional Differential Equations ◽  
Iteration Method ◽  
Fractional Derivatives ◽  
Variational Iteration Method ◽  
Variational Iteration ◽  
Promising Tool ◽  
Approximate Analytical Solutions ◽  
Fractional Differential ◽  
Linear And Nonlinear

This paper presents approximate analytical solutions for the fractional-order Brusselator system using the variational iteration method. The fractional derivatives are described in the Caputo sense. This method is based on the incorporation of the correction functional for the equation. Two examples are solved as illustrations, using symbolic computation. The numerical results show that the introduced approach is a promising tool for solving system of linear and nonlinear fractional differential equations.

scholarly journals The Approximate Solutions of Three-Dimensional Diffusion and Wave Equations within Local Fractional Derivative Operator

2016 ◽  
Vol 2016 ◽  
pp. 1-5 ◽  
Author(s):  
Hassan Kamil Jassim
Keyword(s):  
Fractional Derivative ◽  
Wave Equations ◽  
Three Dimensional ◽  
Variational Iteration Method ◽  
Approximate Solutions ◽  
Derivative Operator ◽  
Transform Method ◽  
Local Fractional Derivative ◽  
Variational Iteration ◽  
Dimensional Diffusion

We used the local fractional variational iteration transform method (LFVITM) coupled by the local fractional Laplace transform and variational iteration method to solve three-dimensional diffusion and wave equations with local fractional derivative operator. This method has Lagrange multiplier equal to minus one, which makes the calculations more easily. The obtained results show that the presented method is efficient and yields a solution in a closed form. Illustrative examples are included to demonstrate the high accuracy and fast convergence of this new method.

Solve fractional differential equations via a hybrid method between variational iteration method and gray wolf optimization algorithm

2020 ◽  
pp. 2150144
Author(s):  
Ahmed Entesar ◽  
Omar Saber Qasim
Keyword(s):  
Differential Equations ◽  
Fractional Differential Equations ◽  
Hybrid Method ◽  
Optimization Algorithm ◽  
Iteration Method ◽  
Optimal Parameter ◽  
Variational Iteration Method ◽  
Gray Wolf ◽  
Variational Iteration ◽  
Fractional Differential

In this paper, a hybrid method between Variational Iteration Method (VIM) and gray wolf optimization algorithm (GWO) was proposed to solve the fractional differential equations (FDE), where the optimal parameter value ([Formula: see text] for the VIM was estimated by the GWO. The solutions in the proposed method, GWO-VIM, demonstrated the efficiency and reliability compared to the default method VIM, by calculating the maximum absolute errors (MAE) and mean square error (MSE).

scholarly journals A new approach for solving systems of fractional differential equations via natural transform

2016 ◽  
Vol 12 (1) ◽  
pp. 5797-5804 ◽  
Author(s):  
A. S Abedl Rady ◽  
S. Z Rida ◽  
A. A. M Arafa ◽  
H. R Abedl Rahim
Keyword(s):  
Nonlinear Systems ◽  
Differential Equations ◽  
Fractional Differential Equations ◽  
Variational Iteration Method ◽  
New Method ◽  
Transform Method ◽  
Variational Iteration ◽  
Fractional Differential ◽  
Linear And Nonlinear ◽  
Linear And Nonlinear Systems

In this paper, A new method proposed and coined by the authors as the natural variational iteration  transform method(NVITM) is utilized to solve linear and nonlinear systems of fractional differential equations. The new method is a combination of natural transform method and variational iteration method. The solutions of our modeled systems are calculated in the form of convergent power series with easily computable components. The numerical results shows that the approach is easy to implement and accurate when applied to various linear and nonlinear systems of fractional differential equations.

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