H-Derivative of the Function and the Fractal Dynamics

In this paper, Hausdorff measure of the function f(x) and H-derivative of the function f(x) under Hausdorff measure are given as follows: HD[f(x)]= supn{nj=1|f(xj)-f(xj-1)|D} and f(1)H(x,0)=limx0[|f(x0+ x)-f(x0+ x)|D]/(2x)D=|f(x0)|D. The system of evolution equation of fractal dynamics is u(1)Ht=k(x)u(2)Hxx-u(1)Hx, dD/dt=f(p1, p2), where the first equation is called the equation of fractal dynamics, and the second equation is called the evolution equation of Hausdorff dimension D.