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Advances in Mathematical Physics
Volume 2013 (2013), Article ID 498789, 7 pages
Complexity and the Fractional Calculus
1Center for Nonlinear Science, University of North Texas, P.O. Box 311427, Denton, TX 76203-1427, USA
2Instituto de Alta Investigación, Universidad de Tarapacá, Casilla 6-D, Arica, Chile
3Information Science Directorate, Army Research Office, Research Triangle Park, NC 27709, USA
Received 21 March 2013; Accepted 28 March 2013
Academic Editor: Dumitru Baleanu
Copyright © 2013 Pensri Pramukkul et al. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.
Citations to this Article [15 citations]
The following is the list of published articles that have cited the current article.
- R. F. Rodríguez, J. Fujioka, and E. Salinas-Rodríguez, “Fractional fluctuation effects on the light scattered by a viscoelastic suspension,” Physical Review E, vol. 88, no. 2, 2013.
- A. Svenkeson, M.T. Beig, M. Turalska, B.J. West, and P. Grigolini, “Fractional trajectories: Decorrelation versus friction,” Physica A: Statistical Mechanics and its Applications, 2013.
- Marzieh Zare, and Paolo Grigolini, “Criticality and avalanches in neural networks,” Chaos, Solitons & Fractals, 2013.
- Mauro Bologna, Bruce West, and Paolo Grigolini, “Renewal and memory origin of anomalous diffusion: A discussion of their joint action,” Physical Review E, vol. 88, no. 6, 2013.
- Mauro Bologna, Adam Svenkeson, Bruce J. West, and Paolo Grigolini, “Diffusion in heterogeneous media: An iterative scheme for finding approximate solutions to fractional differential equations with time-dependent coefficients,” Journal of Computational Physics, 2014.
- Gianni Pagnini, “Short Note on the emergence of fractional kinetics,” Physica A: Statistical Mechanics and its Applications, 2014.
- Bruce West, “A Fractional Probability Calculus View of Allometry,” Systems, vol. 2, no. 2, pp. 89–118, 2014.
- Pensri Pramukkul, Adam Svenkeson, and Paolo Grigolini, “Effect of noise and detector sensitivity on a dynamical process: Inverse power law and Mittag-Leffler interevent time survival probabilities,” Physical Review E, vol. 89, no. 2, 2014.
- J.A. Tenreiro Machado, “Generalized convolution,” Applied Mathematics and Computation, 2014.
- Paolo Grigolini, “Emergence of biological complexity: Criticality, renewal and memory,” Chaos, Solitons & Fractals, 2015.
- Mauro Bologna, Adam Svenkeson, Bruce J. West, and Paolo Grigolini, “Diffusion in heterogeneous media: An iterative scheme for finding approximate solutions to fractional differential equations with time-dependent coeff,” Journal Of Computational Physics, vol. 293, pp. 297–311, 2015.
- R.F. Rodríguez, J. Fujioka, and E. Salinas-Rodríguez, “Fractional correlation functions in simple viscoelastic liquids,” Physica A: Statistical Mechanics and its Applications, 2015.
- Paolo Paradisi, Giorgio Kaniadakis, and Antonio Maria Scarfone, “The emergence of self-organization in complex systems–Preface,” Chaos, Solitons & Fractals, 2015.
- Elvis Geneston, Rohisha Tuladhar, M. T. Beig, Mauro Bologna, and Paolo Grigolini, “Ergodicity breaking and localization,” Physical Review E, vol. 94, no. 1, 2016.
- J. F. Gómez-Aguilar, and Abdon Atangana, “New insight in fractional differentiation: power, exponential decay and Mittag-Leffler laws and applications,” The European Physical Journal Plus, vol. 132, no. 1, 2017.