The influence of fractality on the time evolution of the diffusion process

H. Şirin, F. Büyükkılıç, H. Ertik and D. Demirhan

Physica A: Statistical Mechanics and its Applications, 2010, vol. 389, issue 10, 2007-2013

Abstract: In the literature, the deviations from standard behaviors of the solutions of the kinetic equation and the analogous diffusion equation are put forward by investigations which are carried out in the frame of fractional mathematics and nonextensive physics. On the other hand, the physical origins of the order of derivative namely α in fractional mathematics and the entropy index q in nonextensive physics are a topic of interest in scientific media. In this study, the solutions of the diffusion equation which have been obtained in the framework of fractional mathematics and nonextensive physics are revised. The diffusion equation is solved by the cumulative diminuation/growth method which has been developed by two of the present authors and physical nature of the parameters α and q are enlightened in connection with fractality of space and the memory effect. It has been emphasized that the mathematical basis of deviations from standard behavior in the distribution functions could be established by fractional mathematics where as the physical mechanism could be revealed using the cumulative diminuation/growth method.

Keywords: Fractional diffusion equation; Fractional kinetic equation; Mittag-Leffler function; Cumulative diminuation/growth processes (search for similar items in EconPapers)
Date: 2010
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Citations: View citations in EconPapers (1)

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Persistent link: https://EconPapers.repec.org/RePEc:eee:phsmap:v:389:y:2010:i:10:p:2007-2013

DOI: 10.1016/j.physa.2010.01.027

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