Fractional integral associated to generalized cookie-cutter set and its physical interpretation
- 7 August 1997
- journal article
- Published by IOP Publishing in Journal of Physics A: General Physics
- Vol. 30 (15) , 5569-5577
- https://doi.org/10.1088/0305-4470/30/15/036
Abstract
This paper is based on Nigmatullin's study. When the `residual' memory set is a generalized cookie-cutter set on , using various hypotheses it is proved that the fractional exponent of a fractional integral is not uniquely determined by the fractal dimension of the generalized cookie-cutter set. It is determined by of self-similar measure (or infinite self-similar measure) on this generalized cookie-cutter set, and can run over all positive real numbers.Keywords
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