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Aging and Rejuvenation with Fractional Derivatives

Gerardo Aquino·Mauro Bologna·Paolo Grigolini·Bruce J. West
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Abstract

We discuss a dynamic procedure that makes the 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 mu in the interval 2 >ta yields ord=mu -2. The intermediate time regime is probably incompatible with a picture based on fractional derivatives, or, at least, with a mono-order fractional derivative.

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Gerardo Aquino, Mauro Bologna, Paolo Grigolini, Bruce J. West. 2004-03-19. Aging and Rejuvenation with Fractional Derivatives. https://doi.org/10.1103/physreve.70.036105

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