caa a22 4500 469035757 CHVBK 20180323132755.0 cr unu---uuuuu 170328e19920301xx s 000 0 eng 10.1007/BF01036529 doi (NATIONALLICENCE)springer-10.1007/BF01036529 Nigmatullin R. aut Fractional integral and its physical interpretation [Elektronische Daten] [R. Nigmatullin] 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 timet. 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 extent the domain of applicability of the fractional derivative concept are obtained. Plenum Publishing Corporation, 1992 Theoretical and Mathematical Physics Kluwer Academic Publishers-Plenum Publishers 90/3(1992-03-01), 242-251 0040-5779 90:3<242 1992 90 11232 https://doi.org/10.1007/BF01036529 text/html Onlinezugriff via DOI 1 research-article jats NATIONALLICENCE 856 40 https://doi.org/10.1007/BF01036529 text/html Onlinezugriff via DOI NATIONALLICENCE 100 1- Nigmatullin R. aut NATIONALLICENCE 773 0- Theoretical and Mathematical Physics Kluwer Academic Publishers-Plenum Publishers 90/3(1992-03-01), 242-251 0040-5779 90:3<242 1992 90 11232 Metadata rights reserved Springer special CC-BY-NC licence nationallicence BK010053 XK010053 XK010000 NATIONALLICENCE NATIONALLICENCE NL-springer