scholarly journals Local Fractional Poisson and Laplace Equations with Applications to Electrostatics in Fractal Domain

2014 ◽  
Vol 2014 ◽  
pp. 1-5 ◽  
Author(s):  
Yang-Yang Li ◽  
Yang Zhao ◽  
Gong-Nan Xie ◽  
Dumitru Baleanu ◽  
Xiao-Jun Yang ◽  
...  
Keyword(s):  
Fractional Calculus ◽  
Cylindrical Coordinates ◽  
Fractal Media ◽  
Laplace Equations ◽  
Local Fractional Calculus ◽  
Fractal Domain

From the local fractional calculus viewpoint, Poisson and Laplace equations were presented in this paper. Their applications to the electrostatics in fractal media are discussed and their local forms in the Cantor-type cylindrical coordinates are also obtained.

scholarly journals On the fractal heat transfer problems with local fractional calculus

2015 ◽  
Vol 19 (5) ◽  
pp. 1867-1871 ◽  
Author(s):  
Duan Zhao ◽  
Xiao-Jun Yang ◽  
H.M. Srivastava
Keyword(s):  
Heat Transfer ◽  
Fractional Calculus ◽  
Nonlinear Oscillator ◽  
Fractal Media ◽  
Local Fractional Calculus ◽  
Transfer Equations ◽  
Linear And Nonlinear ◽  
Transfer Problems ◽  
Homogeneous Linear ◽  
Oscillator Equations

This article investigates several fractal heat transfer problems from the local fractional calculus viewpoint. At low and high excess temperatures, the linear and nonlinear heat-transfer equations are presented. The non-homogeneous linear and nonlinear oscillator equations in fractal heat transfer are discussed. The results are adopted to present the behaviors of the heat transfer in fractal media.

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.

scholarly journals Fractal Dynamical Model of Vehicular Traffic Flow within the Local Fractional Conservation Laws

2014 ◽  
Vol 2014 ◽  
pp. 1-5 ◽  
Author(s):  
Long-Fei Wang ◽  
Xiao-Jun Yang ◽  
Dumitru Baleanu ◽  
Carlo Cattani ◽  
Yang Zhao
Keyword(s):  
Fractional Calculus ◽  
Conservation Laws ◽  
Traffic Flow ◽  
Mathematical Theory ◽  
Conservation Equation ◽  
Vehicular Traffic ◽  
New Model ◽  
Local Fractional Calculus ◽  
Vehicular Traffic Flow ◽  
Fractal Network

We suggest a new model of the scale conservation equation in the mathematical theory of vehicular traffic flow on the fractal network based on the local fractional calculus.

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.

scholarly journals Generalizations of Hölder’s and Some Related Integral Inequalities on Fractal Space

2013 ◽  
Vol 2013 ◽  
pp. 1-9 ◽  
Author(s):  
Guang-Sheng Chen
Keyword(s):  
Fractional Calculus ◽  
Integral Inequality ◽  
Hölder’S Inequality ◽  
Integral Inequalities ◽  
Hölder's Inequality ◽  
Local Fractional Calculus ◽  
Related Integral ◽  
Fractal Space

Based on the local fractional calculus, we establish some new generalizations of Hölder’s inequality. By using it, some related results on the generalized integral inequality in fractal space are investigated in detail.

scholarly journals Signal Processing for Nondifferentiable Data Defined on Cantor Sets: A Local Fractional Fourier Series Approach

2014 ◽  
Vol 2014 ◽  
pp. 1-7 ◽  
Author(s):  
Zhi-Yong Chen ◽  
Carlo Cattani ◽  
Wei-Ping Zhong
Keyword(s):  
Signal Processing ◽  
Fourier Series ◽  
Fractional Calculus ◽  
Present Method ◽  
Continuous Functions ◽  
Cantor Sets ◽  
Point Of View ◽  
Local Fractional Calculus ◽  
Processing Point

From the signal processing point of view, the nondifferentiable data defined on the Cantor sets are investigated in this paper. The local fractional Fourier series is used to process the signals, which are the local fractional continuous functions. Our results can be observed as significant extensions of the previously known results for the Fourier series in the framework of the local fractional calculus. Some examples are given to illustrate the efficiency and implementation of the present method.

Sign in / Sign up

Export Citation Format

Share Document