scholarly journals Local Fractional Laplace Variational Iteration Method for Solving Diffusion and Wave Equations on Cantor Sets within Local Fractional Operators

2015 ◽  
Vol 2015 ◽  
pp. 1-9 ◽  
Author(s):  
Hassan Kamil Jassim ◽  
Canan Ünlü ◽  
Seithuti Philemon Moshokoa ◽  
Chaudry Masood Khalique
Keyword(s):  
Laplace Transform ◽  
Iteration Method ◽  
Wave Equations ◽  
Variational Iteration Method ◽  
Approximate Solutions ◽  
High Accuracy ◽  
Cantor Set ◽  
Cantor Sets ◽  
Fractional Operators ◽  
Variational Iteration

The local fractional Laplace variational iteration method (LFLVIM) is employed to handle the diffusion and wave equations on Cantor set. The operators are taken in the local sense. The nondifferentiable approximate solutions are obtained by using the local fractional Laplace variational iteration method, which is the coupling method of local fractional variational iteration method and Laplace transform. Illustrative examples are included to demonstrate the high accuracy and fast convergence of this new algorithm.

scholarly journals Local fractional variational iteration method for Fokker-Planck equation on a Cantor set

2013 ◽  
Vol 23 ◽  
pp. 3-8 ◽  
Author(s):  
Xiao Jun Yang ◽  
Dumitru Baleanu
Keyword(s):  
Iteration Method ◽  
Planck Equation ◽  
Variational Iteration Method ◽  
Cantor Set ◽  
Cantor Sets ◽  
Transform Method ◽  
Variational Iteration ◽  
Fokker Planck Equation ◽  
Fractal Functions ◽  
Fokker Planck

Recently the local fractional operators have started to be considered a useful tool to deal with fractal functions defined on Cantor sets. In this paper, we consider the Fokker-Planck equation on a Cantor set derived from the fractional complex transform method. Additionally, the solution obtained is considered by using the local fractional variational iteration method.

scholarly journals Local Fractional Laplace Variational Iteration Method for Fractal Vehicular Traffic Flow

2014 ◽  
Vol 2014 ◽  
pp. 1-7 ◽  
Author(s):  
Yang Li ◽  
Long-Fei Wang ◽  
Sheng-Da Zeng ◽  
Yang Zhao
Keyword(s):  
Partial Differential Equations ◽  
Laplace Transform ◽  
Traffic Flow ◽  
Iteration Method ◽  
Present Method ◽  
Variational Iteration Method ◽  
Approximate Solutions ◽  
Vehicular Traffic ◽  
Variational Iteration ◽  
Vehicular Traffic Flow

We discuss the line partial differential equations arising in fractal vehicular traffic flow. The nondifferentiable approximate solutions are obtained by using the local fractional Laplace variational iteration method, which is the coupling method of local fractional variational iteration method and Laplace transform. The obtained results show the efficiency and accuracy of implements of the present method.

scholarly journals Comment on “An Approximation to Solution of Space and Time Fractional Telegraph Equations by He's Variational Iteration Method”

2013 ◽  
Vol 2013 ◽  
pp. 1-2
Author(s):  
Yi-Hong Wang ◽  
Lan-Lan Huang
Keyword(s):  
Laplace Transform ◽  
Iteration Method ◽  
Variational Iteration Method ◽  
Approximate Solutions ◽  
Telegraph Equation ◽  
Variational Iteration ◽  
Space And Time ◽  
Fractional Telegraph Equation ◽  
Telegraph Equations ◽  
He’S Variational Iteration Method

The variational iteration method was applied to the time fractional telegraph equation and some variational iteration formulae were suggested in (Sevimlican, 2010). Those formulae are improved by Laplace transform from which the approximate solutions of higher accuracies can be obtained.

scholarly journals Reconstructive schemes for variational iteration method within Yang-Laplace transform with application to fractal heat conduction problem

2013 ◽  
Vol 17 (3) ◽  
pp. 715-721 ◽  
Author(s):  
Chun-Feng Liu ◽  
Shan-Shan Kong ◽  
Shu-Juan Yuan
Keyword(s):  
Heat Conduction ◽  
Laplace Transform ◽  
Fractional Derivative ◽  
Lagrange Multiplier ◽  
Iteration Method ◽  
Heat Conduction Equation ◽  
Heat Conduction Problem ◽  
Variational Iteration Method ◽  
High Accuracy ◽  
Variational Iteration

A reconstructive scheme for variational iteration method using the Yang-Laplace transform is proposed and developed with the Yang-Laplace transform. The identification of fractal Lagrange multiplier is investigated by the Yang-Laplace transform. The method is exemplified by a fractal heat conduction equation with local fractional derivative. The results developed are valid for a compact solution domain with high accuracy.

scholarly journals Variational Approximate Solutions of Fractional Nonlinear Nonhomogeneous Equations with Laplace Transform

2013 ◽  
Vol 2013 ◽  
pp. 1-9
Author(s):  
Yanqin Liu ◽  
Fengsheng Xu ◽  
Xiuling Yin
Keyword(s):  
Laplace Transform ◽  
Perturbation Method ◽  
Lagrange Multiplier ◽  
Iteration Method ◽  
Homotopy Perturbation Method ◽  
Variational Iteration Method ◽  
Approximate Solutions ◽  
Variational Iteration ◽  
Homotopy Perturbation ◽  
The Laplace Transform

A novel modification of the variational iteration method is proposed by means of Laplace transform and homotopy perturbation method. The fractional lagrange multiplier is accurately determined by the Laplace transform and the nonlinear one can be easily handled by the use of He’s polynomials. Several fractional nonlinear nonhomogeneous equations are analytically solved as examples and the methodology is demonstrated.

scholarly journals Variational iteration method for studying perihelion precession and deflection of light in General Relativity

2016 ◽  
Vol 4 (2) ◽  
pp. 52 ◽  
Author(s):  
V.K. Shchigolev
Keyword(s):  
General Relativity ◽  
Iteration Method ◽  
Variational Iteration Method ◽  
Approximate Solutions ◽  
Simple Problem ◽  
Geodesic Equations ◽  
Variational Iteration ◽  
Deflection Of Light ◽  
Perihelion Shift ◽  
Main Ideas

A new approach in studying the planetary orbits and deflection of light in General Relativity (GR) by means of the Variational iteration method (VIM) is proposed in this paper. For this purpose, a brief review of the nonlinear geodesic equations in the spherical symmetry spacetime and the main ideas of VIM are given. The appropriate correct functionals are constructed for the geodesics in the spacetime of Schwarzschild, Reissner-Nordström and Kiselev black holes. In these cases, the Lagrange multiplier is obtained from the stationary conditions for the correct functionals. Then, VIM leads to the simple problem of computation of the integrals in order to obtain the approximate solutions of the geodesic equations. On the basis of these approximate solutions, the perihelion shift and the light deflection have been obtained for the metrics mentioned above.

scholarly journals Analytical solution to local fractional Landau-Ginzburg-Higgs equation on fractal media

2021 ◽  
Vol 25 (6 Part B) ◽  
pp. 4449-4455
Author(s):  
Shu-Xian Deng ◽  
Xin-Xin Ge
Keyword(s):  
Analytical Solution ◽  
Laplace Transform ◽  
Present Article ◽  
Iteration Method ◽  
Variational Iteration Method ◽  
Laplace Transform Method ◽  
Transform Method ◽  
Variational Iteration ◽  
Fractal Media

The main objective of the present article is to introduce a new analytical solution of the local fractional Landau-Ginzburg-Higgs equation on fractal media by means of the local fractional variational iteration transform method, which is coupling of the variational iteration method and Yang-Laplace transform method.

A modified variational iteration method for solving fractional Riccati differential equation by Adomian polynomials

2013 ◽  
Vol 16 (1) ◽  
Author(s):  
Hossein Jafari ◽  
Hale Tajadodi ◽  
Dumitru Baleanu
Keyword(s):  
Differential Equation ◽  
Iteration Method ◽  
Variational Iteration Method ◽  
Approximate Solutions ◽  
Convergence Region ◽  
Riccati Differential Equation ◽  
Adomian Polynomials ◽  
Riccati Differential Equations ◽  
Variational Iteration ◽  
Modified Variational Iteration Method

AbstractIn this paper, we introduce a modified variational iteration method (MVIM) for solving Riccati differential equations. Also the fractional Riccati differential equation is solved by variational iteration method with considering Adomians polynomials for nonlinear terms. The main advantage of the MVIM is that it can enlarge the convergence region of iterative approximate solutions. Hence, the solutions obtained using the MVIM give good approximations for a larger interval. The numerical results show that the method is simple and effective.

scholarly journals Local Fractional Variational Iteration Method for Local Fractional Poisson Equations in Two Independent Variables

2014 ◽  
Vol 2014 ◽  
pp. 1-7 ◽  
Author(s):  
Li Chen ◽  
Yang Zhao ◽  
Hossein Jafari ◽  
J. A. Tenreiro Machado ◽  
Xiao-Jun Yang
Keyword(s):  
Iteration Method ◽  
Fractional Derivatives ◽  
Variational Iteration Method ◽  
Approximate Solutions ◽  
Mathematical Physics ◽  
Nondifferentiable Functions ◽  
Independent Variables ◽  
Poisson Equations ◽  
Variational Iteration ◽  
Two Independent Variables

The local fractional Poisson equations in two independent variables that appear in mathematical physics involving the local fractional derivatives are investigated in this paper. The approximate solutions with the nondifferentiable functions are obtained by using the local fractional variational iteration method.

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