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

Author

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

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.

Suggested Citation

  • Şirin, H. & Büyükkılıç, F. & Ertik, H. & Demirhan, D., 2010. "The influence of fractality on the time evolution of the diffusion process," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 389(10), pages 2007-2013.
    • Handle: RePEc:eee:phsmap:v:389:y:2010:i:10:p:2007-2013
    DOI: 10.1016/j.physa.2010.01.027
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    Cited by:

    1. Şirin, Hüseyin & Büyükkılıç, Fevzi & Ertik, Hüseyin & Demirhan, Doğan, 2011. "The effect of time fractality on the transition coefficients: Historical Stern–Gerlach experiment revisited," Chaos, Solitons & Fractals, Elsevier, vol. 44(1), pages 43-47.

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