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The relationship between the fractional integral and the fractal structure of a memory set

Author

Listed:
  • Ren, Fu-Yao
  • Yu, Zu-Guo
  • Zhou, Ji
  • Mehaute, Alain Le
  • Nigmatullin, Raoul R.

Abstract

It is shown that there is no direct relation between the fractional exponent v of the fractional integral and the fractal structure of the memory set considered, v depends only the first contraction coefficient χ1 and the first weight P1 of the self-similar measure (or infinite self-similar measure) μ on the memory set. If and only if P1=χ1β (where β ∈ (0,1) is the fractal dimension of the memory set), v is equal to the fractal dimension of the memory set. It is also true that v is continuous about χ1 and P1.

Suggested Citation

  • Ren, Fu-Yao & Yu, Zu-Guo & Zhou, Ji & Mehaute, Alain Le & Nigmatullin, Raoul R., 1997. "The relationship between the fractional integral and the fractal structure of a memory set," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 246(3), pages 419-429.
    • Handle: RePEc:eee:phsmap:v:246:y:1997:i:3:p:419-429
    DOI: 10.1016/S0378-4371(97)00353-1
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