We found a match
Your institution may have access to this item. Find your institution then sign in to continue.
- Title
Probability Interpretation of the Integral of Fractional Order.
- Authors
Stanislavsky, A. A.
- Abstract
We establish a relation between stable distributions in probability theory and the fractional integral. Moreover, it turns out that the parameter of the stable distribution coincides with the exponent of the fractional integral. It follows from an analysis of the obtained results that equations with the fractional time derivative describe the evolution of some physical system whose time degree of freedom becomes stochastic, i.e., presents a sum of random time intervals subject to a stable probability distribution. We discuss relations between the fractal Cantor set (Cantor strips) and the fractional integral. We show that the possibility to use this relation as an approximation of the fractional integral is rather limited.
- Subjects
FREE probability theory; FRACTIONAL integrals; INTEGRAL calculus; ANALYSIS of variance; CANTOR sets; OPERATOR algebras
- Publication
Theoretical & Mathematical Physics, 2004, Vol 138, Issue 3, p418
- ISSN
0040-5779
- Publication type
Article
- DOI
10.1023/B:TAMP.0000018457.70786.36