《A generalized model for Yang-Fourier transforms in fractal space_AITS》.pdf

Advances in Intelligent Transportation Systems (AITS) 80 Vol. 1, No. 4, 2012, ISSN 2167-6399 Copyright © World Science Publisher, United States A generalized model for Yang-Fourier transforms in fractal space Xiao-Jun Yang Department of Mathematics Mechanics, China University of Mining Technology, Xuzhou, 221008, P. R. China Email: dyangxiaojun@ Abstract –Local fractional calculus deals with everywhere continuous but nowhere differentiable functions in fractal space. The Yang-Fourier transform based on the local fractional calculus is a generalization of Fourier transform in fractal space. In this paper, local fractional continuous non-differentiable functions in fractal space are studied, and the generalized model for the Yang-Fourier transforms derived from the local fractional calculus are introduced. A generalized model for the Yang-Fourier transforms in fractal space and some results are proposed in detail. Keywords – Local fractional calculus; Local fractional continuous non-differentiable functions; Yang-Fourier transforms; Fractal space 1. Introduction f x C a ,b . (2.2)      Local fractional calculus has been revealed a useful Definition 2 tool in areas ranging from fundamental science to A function f x is called a non-differentiable function engin