A short introduction to Yang-Laplace Transforms in fractal space

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.

[1]  Xiao-Jun Yang.  The Discrete Yang-Fourier Transforms in Fractal Space , 2012 .

[2]  Xiaojun Yang,et al.  Local Fractional Fourier's Transform Based on the Local Fractional Calculus , 2010, 2010 International Conference on Electrical and Control Engineering.

[3]  Y. Xiaojun,et al.  The fundamentals of local fractional derivative of the one-variable non-differentiable functions , 2009 .

[4]  Pietro Cornetti,et al.  On the mechanics of quasi-brittle materials with a fractal microstructure , 2003 .

[5]  Pietro Cornetti,et al.  A fractional calculus approach to the description of stress and strain localization in fractal media , 2002 .

[6]  Guang-Sheng Chen,et al.  Mean value theorems for Local fractional integrals on fractal space , 2011 .

[7]  Xiao-jun Yang,et al.  Fundamentals of Local Fractional Iteration of the Continuously Nondifferentiable Functions Derived from Local Fractional Calculus , 2011, CSIE 2011.

[8]  Xiao-Jun Yang.  Local Fractional Laplace’s Transform Based on the Local Fractional Calculus , 2011, CSIE 2011.

[9]  Xiao-Jun Yang,et al.  Local Fractional Integral Transforms , 2011 .

[10]  Kiran M. Kolwankar,et al.  Fractional differentiability of nowhere differentiable functions and dimensions. , 1996, Chaos.

[11]  Feng Gao,et al.  Local Fractional Newton's Method Derived from Modified Local Fractional Calculus , 2009, 2009 International Joint Conference on Computational Sciences and Optimization.

[12]  J. Schiff.  The Laplace Transform: Theory and Applications , 1999 .

[13]  Varsha Daftardar-Gejji,et al.  On calculus of local fractional derivatives , 2002 .

[14]  Jacky Cresson,et al.  About Non-differentiable Functions , 2001 .

[15]  Guangsheng Chen.  Local fractional improper integral on fractal space , 2012, IAIT 2012.

[16]  Yang Xiao-Jun.  Local Fractional Functional Analysis and Its Applications , 2011 .

[17]  X. Yang,et al.  PROBLEMS OF LOCAL FRACTIONAL DEFINITE INTEGRAL OF THE ONEVARIABLE NONDIFFERENTIABLE FUNCTION , 2009 .