scholarly journals The local fractional iteration solution for the diffusion problem in fractal media

2016 ◽  
Vol 20 (suppl. 3) ◽  
pp. 743-746 ◽  
Author(s):  
Ya-Juan Hao ◽  
Ai-Min Yang
Keyword(s):  
Laplace Transform ◽  
Fractional Derivative ◽  
Diffusion Problem ◽  
Coupling Method ◽  
Iteration Algorithm ◽  
Local Fractional Derivative ◽  
Variational Iteration ◽  
Fractal Media ◽  
First Time

In this paper, we address the coupling method for the local fractional variational iteration algorithm III and local fractional Laplace transform for the first time, which is called as the local fractional Laplace transform variational iteration algorithm III. The proposed technology is used to find the local fractional iteration solution for the diffusion problem in fractal media via local fractional derivative.

scholarly journals A new fractional derivative model for the anomalous diffusion problem

2019 ◽  
Vol 23 (Suppl. 3) ◽  
pp. 1005-1011
Author(s):  
Zhanqing Chen ◽  
Peitao Qiu ◽  
Xiao-Jun Yang ◽  
Yiying Feng ◽  
Jiangen Liu
Keyword(s):  
Heat Conduction ◽  
Analytical Solution ◽  
Laplace Transform ◽  
Fractional Derivative ◽  
Anomalous Diffusion ◽  
Heat Conduction Problem ◽  
Diffusion Problem ◽  
The Laplace Transform ◽  
Complex Phenomena ◽  
First Time

In this paper, a new fractional derivative within the exponential decay kernel is addressed for the first time. A new anomalous diffusion model is proposed to describe the heat-conduction problem. With the use of the Laplace transform, the analytical solution is discussed in detail. The presented result is as an accurate and efficient approach proposed for the heat-conduction problem in the complex phenomena.

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.

ON A HIGH-PASS FILTER DESCRIBED BY LOCAL FRACTIONAL DERIVATIVE

Fractals ◽  
2020 ◽  
Vol 28 (03) ◽  
pp. 2050031 ◽  
Author(s):  
KANG-JIA WANG
Keyword(s):  
Transfer Function ◽  
Laplace Transform ◽  
Fractional Derivative ◽  
Pass Filter ◽  
Electrical Circuits ◽  
Local Fractional Derivative ◽  
High Pass Filter ◽  
Fractal Space ◽  
High Pass

The local fractional derivative (LFD) has gained much interest recently in the field of electrical circuits. This paper proposes a non-differentiable (ND) model of high-pass filter described by the LFD, where the ND transfer function is obtained with the help of the local fractional Laplace transform, and its parameters and properties are studied. The obtained results reveal the sufficiency of the LFD for analyzing circuit systems in fractal space.

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.

scholarly journals Local fractional derivative: A powerful tool to model the fractal differential equation

2019 ◽  
Vol 23 (3 Part A) ◽  
pp. 1703-1706 ◽  
Author(s):  
Shawen Yao ◽  
Kangle Wang
Keyword(s):  
Differential Equation ◽  
Fractional Derivative ◽  
Differential Transform Method ◽  
Transform Method ◽  
Fractal Sets ◽  
Local Fractional Derivative ◽  
Differential Transform ◽  
Fractal Differential Equation ◽  
First Time ◽  
Whitham Equation

In this paper, the modified Fornberg-Whitham equation is described by the local fractional derivative for the first time. The fractal complex transform and the modified reduced differential transform method are successfully adopted to solve the modified local Fornberg-Whitham equation defined on fractal sets.

scholarly journals The integrating factor method for solving the steady heat transfer problems in fractal media

2016 ◽  
Vol 20 (suppl. 3) ◽  
pp. 729-733
Author(s):  
Shan-Xiong Chen ◽  
Zhi-Hao Tang ◽  
Hai-Ning Wang
Keyword(s):  
Heat Transfer ◽  
Fractional Derivative ◽  
Integrating Factor ◽  
Factor Method ◽  
Fractal Media ◽  
Transfer Equations ◽  
Constant Coefficients ◽  
Transfer Problems ◽  
First Time ◽  
Steady Heat

In this paper, we propose the integrating factor method via local fractional derivative for the first time. We use the proposed method to handle the steady heat-transfer equations in fractal media with the constant coefficients. Finally, we discuss the non-differentiable behaviors of fractal heat-transfer problems.

scholarly journals Local Fractional Variational Iteration and Decomposition Methods for Wave Equation on Cantor Sets within Local Fractional Operators

2014 ◽  
Vol 2014 ◽  
pp. 1-6 ◽  
Author(s):  
Dumitru Baleanu ◽  
J. A. Tenreiro Machado ◽  
Carlo Cattani ◽  
Mihaela Cristina Baleanu ◽  
Xiao-Jun Yang
Keyword(s):  
Wave Equation ◽  
Differential Equations ◽  
Fractional Derivative ◽  
Decomposition Methods ◽  
Cantor Set ◽  
Cantor Sets ◽  
Fractional Operators ◽  
Local Fractional Derivative ◽  
Variational Iteration

We perform a comparison between the fractional iteration and decomposition methods applied to the wave equation on Cantor set. The operators are taken in the local sense. The results illustrate the significant features of the two methods which are both very effective and straightforward for solving the differential equations with local fractional derivative.

scholarly journals A new RLC series-resonant circuit modeled by local fractional derivative

2021 ◽  
Vol 25 (6 Part B) ◽  
pp. 4569-4576
Author(s):  
Mei Dong ◽  
Cui-Ling Li ◽  
Wu-Fa Chen ◽  
Guo-Qian Li ◽  
Kang-Jia Wang
Keyword(s):  
Fractional Derivative ◽  
Angular Frequency ◽  
Resonant Circuit ◽  
New Order ◽  
Imped Ance ◽  
Local Fractional Derivative ◽  
Series Resonant ◽  
Input Signals ◽  
Lumped Elements ◽  
First Time

The local fractional derivative has gained more and more attention in the field of fractal electrical circuits. In this paper, we propose a new ?-order RLC** resonant circuit described by the local fractional derivative for the first time. By studying the non-differentiable lumped elements, the non-differentiable equivalent imped?ance is obtained with the help of the local fractional Laplace transform. Then the non-differentiable resonant angular frequency is studied and the non-differentiable resonant characteristic is analyzed with different input signals and parameters, where it is observed that the ?-order RLC resonant circuit becomes the ordinary one for the special case when the fractional order ? = 1. The obtained results show that the local fractional derivative is a powerful tool in the description of fractal circuit systems.

scholarly journals The Yang-Laplace Transform for Solving the IVPs with Local Fractional Derivative

2014 ◽  
Vol 2014 ◽  
pp. 1-5 ◽  
Author(s):  
Chun-Guang Zhao ◽  
Ai-Min Yang ◽  
Hossein Jafari ◽  
Ahmad Haghbin
Keyword(s):  
Differential Equations ◽  
Laplace Transform ◽  
Fractional Derivative ◽  
Fractional Differential Equations ◽  
Analytical Solutions ◽  
Local Fractional Derivative ◽  
Fractional Differential

The IVPs with local fractional derivative are considered in this paper. Analytical solutions for the homogeneous and nonhomogeneous local fractional differential equations are discussed by using the Yang-Laplace transform.

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