Calculation of a static potential created by plane fractal cluster

Nigmatullin, Raoul R.; Alekhin, A. P.

doi:10.1016/j.cnsns.2011.03.022

Cited by 2 publications

(1 citation statement)

References 7 publications

Supporting

Mentioning

Contrasting

Order By: Relevance

“…Another interesting possibility in deeper understanding of different self-similar processes is related to conception of the quasi-fractals (Q-fractals). These fractals with another type of scaling were defined on intuitive level (without their proper justification) in paper [14]. So, here we want to show how to consider the self-similar processes and derive the corresponding functional equation that can take place in structures having another type of scaling.…”

Section: Results and New Possibilitiesmentioning

confidence: 99%

The derivation of the generalized functional equations describing self-similar processes

Nigmatullin

Băleanu

2012

fcaa

Self Cite

View full text Add to dashboard Cite

The generalized functional equations describing a wide class of different self-similar processes are derived. These equations follow from the observation that microscopic function describing an initial self-similar process increases monotonically or even cannot have a certain value. The last case implies the behavior of trigonometric functions cos(zξ n ), sin(zξ n ) at ξ > 1 and n >> 1 that can enter to the microscopic function and when the limits of the initial scaling region are increasing and becoming large. The idea to obtain the desired functional equations is based on the approximate decoupling procedure reducing the increasing microscopic function to the linear combination of the same microscopic functions but having smaller scales. Based on this idea the new solutions for the well-known WeierstrassMandelbrot function were obtained. The generalized functional equations derived in this paper will help to increase the limits of applicability in description of a wide class of self-similar processes that exist in nature. The procedure that is presented in this paper allows to understand deeper the relationship between the procedure of the averaging of the smoothed functions on discrete self-similar structures and continuous fractional integrals.MSC 2010 : Primary 28A80; Secondary 26A33

show abstract

Section: Results and New Possibilitiesmentioning

confidence: 99%