Fractional calculus and the evolution of fractal phenomena

被引：99

作者：

Rocco, A ^{[1
]}

West, BJ ^{[1
]}

机构：

[1] Univ N Texas, Ctr Nonlinear Sci, Denton, TX 76203 USA

来源：

PHYSICA A | 1999年 / 265卷 / 3-4期

关键词：

fractal; complex system; fractional calculus;

D O I：

10.1016/S0378-4371(98)00550-0

中图分类号：

O4 [物理学];

学科分类号：

0702 ;

摘要：

It is argued that the evolution of complex phenomena ought to be described by fractional, differential, stochastic equations whose solutions have scaling properties and are therefore random, fractal functions. To support this argument we demonstrate that the fractional derivative (integral) of a generalized Weierstrass function (GWF) is another fractal function with a greater (lesser) fractal dimension. We also determine that the GWF is a solution to such a fractional differential stochastic equation of motion. (C) 1999 Elsevier Science B.V. All rights reserved.

引用

页码：535 / 546

页数：12