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TMF, 1992, Volume 90, Number 3, Pages 354–368 (Mi tmf5547)  

This article is cited in 47 scientific papers (total in 48 papers)

Fractional integral and its physical interpretation

R. R. Nigmatullin

Kazan State University

Abstract: A relationship is established between Cantor's fractal set (Cantor's bars) and a fractional integral. The fractal dimension of the Cantor set is equal to the fractional exponent of the integral. It follows from analysis of the results that equations in fractional derivatives describe the evolution of physical systems with loss, the fractional exponent of the derivative being a measure of the fraction of the states of the system that are preserved during evolution time $t$. Such systems can be classified as systems with “residual” memory, and they occupy an intermediate position between systems with complete memory, on the one hand, and Markov systems, on the other. The use of such equations to describe transport and relaxation processes is discussed. Some generalizations that extend the domain of applicability of the fractional derivative concept are obtained.

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English version:
Theoretical and Mathematical Physics, 1992, 90:3, 242–251

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Received: 31.01.1991

Citation: R. R. Nigmatullin, “Fractional integral and its physical interpretation”, TMF, 90:3 (1992), 354–368; Theoret. and Math. Phys., 90:3 (1992), 242–251

Citation in format AMSBIB
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\paper Fractional integral and its physical interpretation
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\jour Theoret. and Math. Phys.
\yr 1992
\vol 90
\issue 3
\pages 242--251
\crossref{https://doi.org/10.1007/BF01036529}
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