Aging and Rejuvenation with Fractional Derivatives
Abstract
We discuss a dynamic procedure that makes fractional derivatives emerge in the time asymptotic limit of non-Poisson processes. We find that two-state fluctuations, with an inverse power-law distribution of waiting times, finite first moment, and divergent second moment, namely, with the power index micro in the interval 2 < micro < 3, yield a generalized master equation equivalent to the sum of an ordinary Markov contribution and a fractional derivative term. We show that the order of the fractional derivative depends on the age of the process under study. If the system is infinitely old, the order of the fractional derivative, alpha, is given by o=3 micro.
Document Details
- Document Type
- Technical Report
- Publication Date
- Sep 10, 2004
- Accession Number
- ADA434831
Entities
People
- Bruce J. West
- Gerardo Aquino
- Mauro Bologna
- Paolo Grigolini
Organizations
- University of North Texas