《A short introduction to Yang-Laplace Transforms in fractal space_AITM》.pdf

Advances in Information Technology and Management 38 Vol. 1, No. 2, June 2012 Copyright © World Science Publisher, United States A short introduction to Yang-Laplace Transforms in fractal space Xiao-Jun Yang Department of Mathematics and Mechanics, China University of Mining and Technology, Xuzhou Campus, Xuzhou, Jiangsu, 221008, P. R. China Email: dyangxiaojun@163.com Abstract –The Yang-Laplace transforms [W. P. Zhong, F. Gao, In: Proc. of the 2011 3rd International Conference on Computer Technology and Development, 209-213, ASME, 2011] in fractal space is a generalization of Laplace transforms derived from the local fractional calculus. This letter presents a short introduction to Yang-Laplace transforms in fractal space. At first, we present the theory of local fractional derivative and integral of non-differential functions defined on cantor set. Then the properties and theorems for Yang-Laplace transforms are tabled, and both the initial value theorem and the final value theorem are investigated. Finally, some applications to the wave equation and the partial differential equation with local fractional derivative are studied in detail. Keywords –Yang-Laplace transforms; Local fractional calculus; Fractal space; Non-differential functions, Initial and final value theorem; Cantor set  1. Introduction I   f x a b  