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Full-Text Articles in Physical Sciences and Mathematics
The Discrete Yang-Fourier Transforms In Fractal Space, Yang Xiao-Jun
The Discrete Yang-Fourier Transforms In Fractal Space, Yang Xiao-Jun
Xiao-Jun Yang
The Yang-Fourier transform (YFT) in fractal space is a generation of Fourier transform based on the local fractional calculus. The discrete Yang-Fourier transform (DYFT) is a specific kind of the approximation of discrete transform, used in Yang-Fourier transform in fractal space. This paper points out new standard forms of discrete Yang-Fourier transforms (DYFT) of fractal signals, and both properties and theorems are investigated in detail.
Asymptotic Methods For Solitary Solutions And Compactons, Ji-Huan He
Asymptotic Methods For Solitary Solutions And Compactons, Ji-Huan He
Ji-Huan He
This review is an elementary introduction to some new asymptotic methods for the search for the solitary solutions of nonlinear differential equations, nonlinear differential-difference equations, and nonlinear fractional differential equations . Particular attention is paid throughout the paper to giving an intuitive grasp for the variational approach, the Hamiltonian approach, the variational iteration method, the homotopy perturbation method, the parameter-expansion method, the Yang-Laplace Transform, the Yang-Fourier transform, and ancient Chinese mathematics. Hamilton principle and variational principles are also emphasized. The reviewed asymptotic methods are easy to be followed for various applications. Some ideas on this review article are first appeared. …