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Articles 1 - 18 of 18
Full-Text Articles in Physical Sciences and Mathematics
Maxwell’S Equations On Cantor Sets: A Local Fractional Approach, Yang Xiaojun
Maxwell’S Equations On Cantor Sets: A Local Fractional Approach, Yang Xiaojun
Xiao-Jun Yang
Maxwell’s equations on Cantor sets are derived from the local fractional vector calculus. It is shown that Maxwell’s equations on Cantor sets in a fractal bounded domain give efficiency and accuracy for describing the fractal electric and magnetic fields. Local fractional differential forms of Maxwell’s equations on Cantor sets in the Cantorian and Cantor-type cylindrical coordinates are obtained. Maxwell’s equations on Cantor set with local fractional operators are the first step towards a unified theory of Maxwell’s equations for the dynamics of cold dark matter.
Application Of The Local Fractional Series Expansion Method And The Variational Iteration Method To The Helmholtz Equation Involving Local Fractional Derivative Operators, Yang Xiaojun
Xiao-Jun Yang
We investigate solutions of the Helmholtz equation involving local fractional derivative operators. We make use of the series expansion method and the variational iteration method, which are based upon the local fractional derivative operators. The nondifferentiable solution of the problem is obtained by using these methods.
Mappings For Special Functions On Cantor Sets And Special Integral Transforms Via Local Fractional Operators, Yang Xiaojun
Mappings For Special Functions On Cantor Sets And Special Integral Transforms Via Local Fractional Operators, Yang Xiaojun
Xiao-Jun Yang
The mappings for some special functions on Cantor sets are investigated. Meanwhile, we apply the local fractional Fourier series, Fourier transforms, and Laplace transforms to solve three local fractional differential equations, and the corresponding nondifferentiable solutions were presented.
Approximation Solutions For Local Fractional Schrödinger Equation In The One-Dimensional Cantorian System, Xiao-Jun Yang
Approximation Solutions For Local Fractional Schrödinger Equation In The One-Dimensional Cantorian System, Xiao-Jun Yang
Xiao-Jun Yang
The local fractional Schr¨odinger equations in the one-dimensional Cantorian systemare investigated.The approximations solutions are obtained by using the local fractional series expansion method. The obtained solutions show that the present method is an efficient and simple tool for solving the linear partial differentiable equations within the local fractional derivative.
Helmholtz And Diffusion Equations Associated With Local Fractional Derivative Operators Involving The Cantorian And Cantor-Type Cylindrical Coordinates, Yang Xiaojun
Xiao-Jun Yang
The main object of this paper is to investigate the Helmholtz and diffusion equations on the Cantor sets involving local fractional derivative operators. The Cantor-type cylindrical-coordinate method is applied to handle the corresponding local fractional differential equations. Two illustrative examples for the Helmholtz and diffusion equations on the Cantor sets are shown by making use of the Cantorian and Cantor-type cylindrical coordinates.
A New Neumann Series Method For Solving A Family Of Local Fractional Fredholm And Volterra Integral Equations, Xiao-Jun Yang
A New Neumann Series Method For Solving A Family Of Local Fractional Fredholm And Volterra Integral Equations, Xiao-Jun Yang
Xiao-Jun Yang
We propose a new Neumann series method to solve a family of local fractional Fredholm and Volterra integral equations. The integral operator, which is used in our investigation, is of the local fractional integral operator type. Two illustrative examples show the accuracy and the reliability of the obtained results.
Analysis Of Fractal Wave Equations By Local Fractional Fourier Series Method, Xiao-Jun Yang
Analysis Of Fractal Wave Equations By Local Fractional Fourier Series Method, Xiao-Jun Yang
Xiao-Jun Yang
The fractal wave equations with local fractional derivatives are investigated in this paper.The analytical solutions are obtained by using local fractional Fourier series method. The present method is very efficient and accurate to process a class of local fractional differential equations.
Systems Of Navier-Stokes Equations On Cantor Sets
Systems Of Navier-Stokes Equations On Cantor Sets
Xiao-Jun Yang
We present systems of Navier-Stokes equations on Cantor sets, which are described by the local fractional vector calculus. It is shown that the results for Navier-Stokes equations in a fractal bounded domain are efficient and accurate for describing fluid flow in fractal media.
Local Fractional Series Expansion Method For Solving Wave And Diffusion Equations On Cantor Sets, Yang Xiaojun
Local Fractional Series Expansion Method For Solving Wave And Diffusion Equations On Cantor Sets, Yang Xiaojun
Xiao-Jun Yang
We proposed a local fractional series expansion method to solve the wave and diffusion equations on Cantor sets. Some examples are given to illustrate the efficiency and accuracy of the proposed method to obtain analytical solutions to differential equations within the local fractional derivatives.
Approximate Solutions For Diffusion Equations On Cantor Space-Time, Xiao-Jun Yang
Approximate Solutions For Diffusion Equations On Cantor Space-Time, Xiao-Jun Yang
Xiao-Jun Yang
In this paper we investigate diffusion equations on Cantor space-time and we obtain approximate solutions by using the local fractional Adomian decomposition method derived from the local fractional operators. Analytical solutions are given in terms of the Mittag-Leffler functions defined on Cantor sets.
1-D Heat Conduction In A Fractal Medium: A Solution By The Local Fractional Fourier Series Method, Xiao-Jun Yang
1-D Heat Conduction In A Fractal Medium: A Solution By The Local Fractional Fourier Series Method, Xiao-Jun Yang
Xiao-Jun Yang
In this communication 1-D heat conduction in a fractal medium is solved by the local fractional Fourier series method. The solution developed allows relating the basic properties of the fractal medium to the local heat transfer mechanism.
Fractional Complex Transform Method For Wave Equations On Cantor Sets Within Local Fractional Differential Operator, Xiao-Jun Yang
Fractional Complex Transform Method For Wave Equations On Cantor Sets Within Local Fractional Differential Operator, Xiao-Jun Yang
Xiao-Jun Yang
This paper points out the fractional complex transform method for wave equations on Cantor sets within the local differential fractional operators. The proposed method is efficient to handle differential equations on Cantor sets.
Damped Wave Equation And Dissipative Wave Equation In Fractal Strings Within The Local Fractional Variational Iteration Method, Xiao-Jun Yang
Damped Wave Equation And Dissipative Wave Equation In Fractal Strings Within The Local Fractional Variational Iteration Method, Xiao-Jun Yang
Xiao-Jun Yang
No abstract provided.
Cantor-Type Cylindrical-Coordinate Method For Differential Equations With Local Fractional Derivatives, Xiao-Jun Yang
Cantor-Type Cylindrical-Coordinate Method For Differential Equations With Local Fractional Derivatives, Xiao-Jun Yang
Xiao-Jun Yang
In this Letter, we propose to use the Cantor-type cylindrical-coordinate method in order to investigate a family of local fractional differential operators on Cantor sets. Some testing examples are given to illustrate the capability of the proposed method for the heat-conduction equation on a Cantor set and the damped wave equation in fractal strings. It is seen to be a powerful tool to convert differential equations on Cantor sets from Cantorian-coordinate systems to Cantor-type cylindrical-coordinate systems.
Fractal Heat Conduction Problem Solved By Local Fractional Variation Iteration Method, Yang Xiaojun
Fractal Heat Conduction Problem Solved By Local Fractional Variation Iteration Method, Yang Xiaojun
Xiao-Jun Yang
This paper points out a novel local fractional variational iteration method for processing the local fractional heat conduction equation arising in fractal heat transfer.
A Local Fractional Variational Iteration Method For Laplace Equation Within Local Fractional Operators, Xiao-Jun Yang
A Local Fractional Variational Iteration Method For Laplace Equation Within Local Fractional Operators, Xiao-Jun Yang
Xiao-Jun Yang
The local fractional variational iteration method for local fractional Laplace equation is investigated in this paper. The operators are described in the sense of local fractional operators.The obtained results reveal that the method is very effective.
One-Phase Problems For Discontinuous Heat Transfer In Fractal Media, Yang Xiaojun
One-Phase Problems For Discontinuous Heat Transfer In Fractal Media, Yang Xiaojun
Xiao-Jun Yang
We first propose the fractal models for the one-phase problems of discontinuous transient heat transfer.The models are taken in sense of local fractional differential operator and used to describe the (dimensionless)melting of fractal solid semi-infinite materials initially at their melt temperatures.
Local Fractional Fourier Series With Application To Wave Equation In Fractal Vibrating String, Yang Xiaojun
Local Fractional Fourier Series With Application To Wave Equation In Fractal Vibrating String, Yang Xiaojun
Xiao-Jun Yang
We introduce the wave equation in fractal vibrating string in the framework of the local fractional calculus. Our particular attention is devoted to the technique of the local fractional Fourier series for processing these local fractional differential operators in a way accessible to applied scientists. By applying this technique we derive the local fractional Fourier series solution of the local fractional wave equation in fractal vibrating string and show the fundamental role of the Mittag- Leffler function.