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 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 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.

Brownian Motion on Cantor Sets

2020 ◽  
Vol 21 (3-4) ◽  
pp. 275-281
Author(s):  
Ali Khalili Golmankhaneh ◽  
Saleh Ashrafi ◽  
Dumitru Baleanu ◽  
Arran Fernandez
Keyword(s):  
Brownian Motion ◽  
Classical Method ◽  
Mean Square Displacement ◽  
Planck Equation ◽  
Cantor Sets ◽  
Mean Square ◽  
Fokker Planck Equation ◽  
Fractal Time ◽  
The Mean ◽  
Fokker Planck

AbstractIn this paper, we have investigated the Langevin and Brownian equations on fractal time sets using Fα-calculus and shown that the mean square displacement is not varied linearly with time. We have also generalized the classical method of deriving the Fokker–Planck equation in order to obtain the Fokker–Planck equation on fractal time sets.

scholarly journals A modification fractional variational iteration method for solving nonlinear gas dynamic and coupled KdV equations involving local fractional operators

2018 ◽  
Vol 22 (Suppl. 1) ◽  
pp. 165-175 ◽  
Author(s):  
Dumitru Baleanu ◽  
Hassan Jassim ◽  
Hasib Khan
Keyword(s):  
Iteration Method ◽  
Variational Iteration Method ◽  
Approximate Solutions ◽  
New Technique ◽  
Transform Method ◽  
Variational Iteration ◽  
Kdv Equations ◽  
Gas Dynamic ◽  
Coupled Kdv Equations ◽  
A New Technique

In this paper, we apply a new technique, namely local fractional variational iteration transform method on homogeneous/non-homogeneous non-linear gas dynamic and coupled KdV equations to obtain the analytical approximate solutions. The iteration procedure is based on local fractional derivative and integral operators. This method is the combination of the local fractional Laplace transform and variational iteration method. The method in general is easy to implement and yields good results. Illustrative examples are included to demonstrate the validity and applicability of the new technique.

scholarly journals Variational Iteration Algorithm-I with an Auxiliary Parameter for Solving Fokker-Planck Equation

2019 ◽  
pp. 29-37 ◽  
Author(s):  
Hijaz Ahmad
Keyword(s):  
Large Class ◽  
Planck Equation ◽  
Suitable Method ◽  
Iteration Algorithm ◽  
Auxiliary Parameter ◽  
Variational Iteration ◽  
Fokker Planck Equation ◽  
Linear Problems ◽  
Fokker Planck Equations ◽  
Fokker Planck

In this paper, variational iteration algorithm-I with an auxiliary parameter is implemented to investigate Fokker-Planck equations. To show the accuracy and reliability of the technique comparisons are made between the variational iteration algorithm-I with an auxiliary parameter and classic variational iteration algorithm-I. The comparison shows that variational iteration algorithm-I with an auxiliary parameter is more powerful and suitable method for solving Fokker-Planck equations. Furthermore, the proposed algorithm can successfully be applied to a large class of nonlinear and linear problems.

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.

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