Journal of Mathematical Sciences

, Volume 89, Issue 5, pp 1570–1575 | Cite as

The fractal nature of the asymptotic solution of an integral equation with stable (in Lévy's sense) kernel

  • V. A. Slobodenyuk
  • V. V. Uchaikin


We consider the asymptotic behavior of the solution\(n (\vec r)\) of a nonhomogeneous integral equation for a threedimensional density with a right-hand side and kernel qp(α), where\((\vec r)\) is the density of a stable (in Lévy's sense) distribution. We demonstrate that the solution is of an asymptotically fractal nature, i.e.
$$n (\vec r) \sim Br^{D - 3} , 0< D< 3,$$
for q=1, α<2, and the fractal dimensionality D coincides with the characteristic of the stable law α.


Integral Equation Asymptotic Behavior Asymptotic Solution Fractal Nature Fractal Dimensionality 
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Copyright information

© Plenum Publishing Corporation 1998

Authors and Affiliations

  • V. A. Slobodenyuk
    • 1
  • V. V. Uchaikin
    • 1
  1. 1.Ulyanovsk State UniversityUlyanovskRussia

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