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摘要: 给出了函数的Hausdorff测度与H-导数。从而，为开展自给的分形动力学提供了解析的数学工具。同时，给出了分形动力学的演化方程组并做了初步讨论与分析。
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关键词:
- 函数的Hausdorf测度 /
- 函数的H-导数 /
- 演化方程组
Abstract: 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. -
Alain le m'ehaut'e. Fractal Geometry, Theory and Application. Jack Howlett Tran. Boca Raten-Ann Arbot-London: CRC Press Inc, 1991. Betal D K. The Fractional Calculus, Theory and Application of Differentiation and Integration to Arbitrany Order. New York: Academia Press, 1974. Feder J. Fractals. New York: Plenum Press, 1988. Besicovitch A S. Proceedings of the Combridge Philosophical Society, 1945, 41: 101. Falconer K J. The Geometry of Fractal Sets. Combridge, New York: Combridge University Press, 1985. -
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