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

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Teoreticheskaya i Matematicheskaya Fizika, 1992, Volume 90, Number 3, Pages 354–368 (Mi tmf5547)

This article is cited in 215 scientific papers (total in 216 papers)

Fractional integral and its physical interpretation

R. R. Nigmatullin

Kazan State University

Full-text PDF (1249 kB) Citations (216)

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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.

Received: 31.01.1991

English version:
Theoretical and Mathematical Physics, 1992, Volume 90, Issue 3, Pages 242–251
DOI: https://doi.org/10.1007/BF01036529

Bibliographic databases:

Language: Russian

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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https://www.mathnet.ru/eng/tmf/v90/i3/p354

Comments

On the paper by R. R. Nigmatullin “Fractional integral and its physical interpretation”
R. S. Rutman
TMF, 1994, 100:3, 476–478

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