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.

The Combined Laplace-Variational Iteration Method for Partial Differential Equations

2013 ◽  
Vol 14 (2) ◽  
Author(s):  
M. Matinfar ◽  
M. Saeidy ◽  
M. Ghasemi
Keyword(s):  
Partial Differential Equations ◽  
Differential Equations ◽  
Laplace Transform ◽  
Iteration Method ◽  
Variational Iteration Method ◽  
Partial Differential ◽  
Transform Method ◽  
Variational Iteration ◽  
Approximate Analytical Solutions ◽  
The Laplace Transform

AbstractIn this paper, the Laplace transform Variational Iteration Method (LVIM) is employed to obtain approximate analytical solutions of the linear and nonlinear partial differential equations. This method is a combined form of the Laplace transform method and the Variational Iteration Method. The proposed scheme, finds the solutions without any discretization or restrictive assumptions and is free from round-off errors and therefore, reduces the numerical computations to a great extent. Some illustrative examples are presented and the numerical results show that the solutions of the LVIM are in good agreement with the exact solution.

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 Variational Iteration Method for Analytical Solution of the Lane-Emden Type Equation with Singular Initial and Boundary Conditions

2019 ◽  
pp. 127-142 ◽  
Author(s):  
Muhammad Nadeem ◽  
Hijaz Ahmad
Keyword(s):  
Exact Solution ◽  
Analytical Solution ◽  
Iteration Method ◽  
Initial Value Problems ◽  
Type Equation ◽  
Variational Iteration Method ◽  
Mathematical Physics ◽  
Initial Value ◽  
Emden Equation ◽  
Variational Iteration

In this paper, a well-known equation used in astrophysics and mathematical physics called the Lane-Emden equation is to be solved by a variational iteration method. The main purpose of this approach is to solve the singular initial value problems and also boundary value problem of Lane-Emden type equations. This technique overcomes its singularity at origin rapidly. It gives the approximate and exact solution with easily computable terms. The approach is illustrated with some examples to show its reliability and compactness.

scholarly journals He’s fractal calculus and its application to fractal KdV equation

2021 ◽  
pp. 100-100
Author(s):  
Xue-Si Ma ◽  
Li-Na Zhang
Keyword(s):  
Analytical Solution ◽  
Iteration Method ◽  
Approximate Analytical Solution ◽  
Kdv Equation ◽  
Variational Iteration Method ◽  
Natural Phenomena ◽  
Transform Method ◽  
Fractal Derivative ◽  
Fractal Calculus ◽  
Fractal Space

He?s fractal calculus is a powerful and effective tool to dealing with natural phenomena in a fractal space. In this paper, we study the fractal KdV equation with He?s fractal derivative. We first adopt the two-scale transform method to convert the fractal KdV equation into its traditional partner in acontinuous space. Finally, we successfully use He?s variational iteration method (HVIM) to obtain its approximate analytical solution.

scholarly journals A New Technique of Laplace Variational Iteration Method for Solving Space-Time Fractional Telegraph Equations

2013 ◽  
Vol 2013 ◽  
pp. 1-10 ◽  
Author(s):  
Fatima A. Alawad ◽  
Eltayeb A. Yousif ◽  
Arbab I. Arbab
Keyword(s):  
Laplace Transform ◽  
Exact Solutions ◽  
Iteration Method ◽  
Variational Iteration Method ◽  
Space Time ◽  
New Techniques ◽  
Variational Iteration ◽  
Telegraph Equations ◽  
A New Technique ◽  
Special Case

In this paper, the exact solutions of space-time fractional telegraph equations are given in terms of Mittage-Leffler functions via a combination of Laplace transform and variational iteration method. New techniques are used to overcome the difficulties arising in identifying the general Lagrange multiplier. As a special case, the obtained solutions reduce to the solutions of standard telegraph equations of the integer orders.

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