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 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 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 remark on local fractional calculus and ordinary derivatives

2016 ◽  
Vol 14 (1) ◽  
pp. 1122-1124 ◽  
Author(s):  
Ricardo Almeida ◽  
Małgorzata Guzowska ◽  
Tatiana Odzijewicz
Keyword(s):  
Fractional Calculus ◽  
Fractional Derivative ◽  
Short Note ◽  
General Definition ◽  
Local Fractional Derivative ◽  
Fundamental Properties ◽  
Local Fractional Calculus ◽  
Definition Of

AbstractIn this short note we present a new general definition of local fractional derivative, that depends on an unknown kernel. For some appropriate choices of the kernel we obtain some known cases. We establish a relation between this new concept and ordinary differentiation. Using such formula, most of the fundamental properties of the fractional derivative can be derived directly.

Development of active filter with series resonant circuit

2003 ◽  
Author(s):  
A. Nakajima ◽  
K. Oku ◽  
J. Nishidai ◽  
T. Shiraishi ◽  
Y. Ogihara ◽  
...  
Keyword(s):  
Active Filter ◽  
Resonant Circuit ◽  
Series Resonant

scholarly journals A Three-Phase Diode Rectifier Having a Series Resonant Circuit on the AC Side

1989 ◽  
Vol 109 (2) ◽  
pp. 130-130
Author(s):  
Toshihiko Tanaka ◽  
Hiroharu Fugou ◽  
Hirofumi Akagi ◽  
Akira Nabae
Keyword(s):  
Resonant Circuit ◽  
Three Phase ◽  
Series Resonant

scholarly journals Mathematical Models Arising in the Fractal Forest Gap via Local Fractional Calculus

2014 ◽  
Vol 2014 ◽  
pp. 1-6 ◽  
Author(s):  
Chun-Ying Long ◽  
Yang Zhao ◽  
Hossein Jafari
Keyword(s):  
Fractional Calculus ◽  
Fractional Derivative ◽  
Mathematical Models ◽  
Cantor Sets ◽  
Forest Gap ◽  
Local Fractional Derivative ◽  
Local Fractional Calculus ◽  
Growth Equations ◽  
Gap Models ◽  
Individual Trees

The forest new gap models via local fractional calculus are investigated. The JABOWA and FORSKA models are extended to deal with the growth of individual trees defined on Cantor sets. The local fractional growth equations with local fractional derivative and difference are discussed. Our results are first attempted to show the key roles for the nondifferentiable growth of individual trees.

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.

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