Complexity and the Fractional Calculus

Abstract

We study complex processes whose evolution in time rests on the occurrence of a large and random number of events. The mean time interval between two consecutive critical events is infinite, thereby violating the ergodic condition and activating at the same time a stochastic central limit theorem that supports the hypothesis that the Mittag-Leffler function is a universal property of nature. The time evolution of these complex systems is properly generated by means of fractional differential equations, thus leading to the interpretation of fractional trajectories as the average over many random trajectories each of which satisfies the stochastic central limit theorem and the condition for the Mittag-Leffler universality.

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Document Details

Document Type
Technical Report
Publication Date
Jan 01, 2013
Accession Number
ADA623103

Entities

People

  • Adam Svenkeson
  • Bruce J. West
  • Mauro Bologna
  • Paolo Grigolini
  • Pensri Pramukkul

Organizations

  • University of North Texas

Tags

DTIC Thesaurus Topics

  • Algorithms
  • Calculus
  • Complex Systems
  • Computational Science
  • Differential Equations
  • Dynamics
  • Equations
  • Equations Of Motion
  • Hiv Infections
  • Information Science
  • Intervals
  • Molecular Mechanics Methods
  • Physics
  • Probability
  • Probability Density Functions
  • Random Variables
  • Time Intervals

Readers

  • Mathematical Modeling and Probability Theory.
  • Theoretical Analysis.