Fractional calculus and the evolution of fractal phenomena

Andrea Rocco and Bruce J. West

Physica A: Statistical Mechanics and its Applications, 1999, vol. 265, issue 3, 535-546

Abstract: 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.

Keywords: Fractal; Complex system; Fractional calculus (search for similar items in EconPapers)
Date: 1999
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Citations: View citations in EconPapers (8)

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Persistent link: https://EconPapers.repec.org/RePEc:eee:phsmap:v:265:y:1999:i:3:p:535-546

DOI: 10.1016/S0378-4371(98)00550-0

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