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Numerical Analysis and Computation Commons™
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Articles 1 - 12 of 12
Full-Text Articles in Numerical Analysis and Computation
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.
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.
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.
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.
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.
A Cauchy Problem For Some Local Fractional Abstract Differential Equation With Fractal Conditions, Yang Xiaojun, Zhong Weiping, Gao Feng
A Cauchy Problem For Some Local Fractional Abstract Differential Equation With Fractal Conditions, Yang Xiaojun, Zhong Weiping, Gao Feng
Xiao-Jun Yang
Fractional calculus is an important method for mathematics and engineering [1-24]. In this paper, we review the existence and uniqueness of solutions to the Cauchy problem for the local fractional differential equation with fractal conditions \[ D^\alpha x\left( t \right)=f\left( {t,x\left( t \right)} \right),t\in \left[ {0,T} \right], x\left( {t_0 } \right)=x_0 , \] where $0<\alpha \le 1$ in a generalized Banach space. We use some new tools from Local Fractional Functional Analysis [25, 26] to obtain the results.