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International Journal of Differential Equations
Volume 2010 (2010), Article ID 104505, 29 pages
The -Wright Function in Time-Fractional Diffusion Processes: A Tutorial Survey
1Department of Physics, University of Bologna and INFN, Via Irnerio 46, 40126 Bologna, Italy
2CRESME Ricerche S.p.A, Viale Gorizia 25C, 00199 Roma, Italy
3CRS4, Centro Ricerche Studi Superiori e Sviluppo in Sardegna, Polaris Building 1, 09010 Pula, Italy
Received 13 September 2009; Accepted 8 November 2009
Academic Editor: Fawang Liu
Copyright © 2010 Francesco Mainardi 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 [34 citations]
The following is the list of published articles that have cited the current article.
- R. K. Saxena, S. L. Kalla, and Ravi Saxena, “Multivariate analogue of generalized Mittag-Leffler function,” Integral Transforms and Special Functions, vol. 22, no. 7, pp. 533–548, 2011.
- Dexter O. Cahoy, “Moment estimators for the two-parameter M-Wright distribution,” Computational Statistics, vol. 27, no. 3, pp. 487–497, 2011.
- G. Pagnini, “The evolution equation for the radius of a premixed flame ball in fractional diffusive media,” European Physical Journal-Special Topics, vol. 193, no. 1, pp. 105–117, 2011.
- Ram K. Saxena, and Gianni Pagnini, “Exact solutions of triple-order time-fractional differential equations for anomalous relaxation and diffusion I: The accelerating case,” Physica A-Statistical Mechanics And Its Applications, vol. 390, no. 4, pp. 602–613, 2011.
- Colin Atkinson, and Adel Osseiran, “Rational Solutions For The Time-Fractional Diffusion Equation,” Siam Journal on Applied Mathematics, vol. 71, no. 1, pp. 92–106, 2011.
- F. F. Dou, and Y. C. Hon, “Kernel-based approximation for Cauchy problem of the time-fractional diffusion equation,” Engineering Analysis With Boundary Elements, vol. 36, no. 9, pp. 1344–1352, 2012.
- Enrico Scalas, and Noelia Viles, “On the convergence of quadratic variation for compound fractional Poisson processes,” Fractional Calculus And Applied Analysis, vol. 15, no. 2, pp. 314–331, 2012.
- Gianni Pagnini, “Erdelyi-Kober Fractional Diffusion,” Fractional Calculus and Applied Analysis, vol. 15, no. 1, pp. 117–127, 2012.
- Mirko D’Ovidio, “From Sturm–Liouville problems to fractional and anomalous diffusions,” Stochastic Processes and their Applications, vol. 122, no. 10, pp. 3513–3544, 2012.
- Dexter O. Cahoy, “Estimation and Simulation for the M-Wright Function,” Communications in Statistics-Theory and Methods, vol. 41, no. 8, pp. 1466–1477, 2012.
- A. Hanyga, and M. Seredyn´ska, “Spatially fractional-order viscoelasticity, non-locality, and a new kind of anisotropy,” Journal of Mathematical Physics, vol. 53, no. 5, pp. 052902, 2012.
- F. S. Costa, and E. Capelas de Oliveira, “Fractional wave-diffusion equation with periodic conditions,” Journal of Mathematical Physics, vol. 53, no. 12, pp. 123520, 2012.
- Mustafa Bayram, and Muhammet Kurulay, “Some properties of the Mittag-Leffler functions and their relation with the Wright functions,” Advances In Difference Equations, 2012.
- Shanoja R. Naik, and Bovas Abraham, “The fractional-diffusion equation and a new distribution to model positively skewed data with heavy tails,” Statistics & Probability Letters, vol. 83, no. 7, pp. 1759–1769, 2013.
- Gianni Pagnini, “The M-Wright function as a generalization of the Gaussian density for fractional diffusion processes,” Fractional Calculus and Applied Analysis, vol. 16, no. 2, pp. 436–453, 2013.
- Gianni Pagnini, Antonio Mura, and Francesco Mainardi, “Two-particle anomalous diffusion: Probability density functions and self-similar stochastic processes,” Philosophical Transactions of the Royal Society A: Mathematical, Physical and Engineering Sciences, vol. 371, no. 1990, 2013.
- Ondrej Vopicka, Karel Friess, Vladimír Hynek, Petr Sysel, Miroslav Zgažar, Milan Šípek, Kryštof Pilnácek, Marek Lanc, Johannes C. Jansen, Christopher R. Mason, and Peter M. Budd, “Equilibrium and transient sorption of vapours and gases in the polymer of intrinsic microporosity PIM-1,” Journal of Membrane Science, vol. 434, pp. 148–160, 2013.
- A. G. Butkovskii, S. S. Postnov, and E. A. Postnova, “Fractional integro-differential calculus and its control-theoretical applications. I. Mathematical fundamentals and the problem of interpretation,” Automation and Remote Control, vol. 74, no. 4, pp. 543–574, 2013.
- Pradeep Kumar, Dwijendra N. Pandey, and D. Bahuguna, “Approximations of Solutions to a Fractional Differential Equation with a Deviating Argument,” Differential Equations and Dynamical Systems, 2013.
- Liyan Wang, and Jijun Liu, “Total variation regularization for a backward time-fractional diffusion problem,” Inverse Problems, vol. 29, no. 11, 2013.
- B. N. Narahari Achar, Bradley T. Yale, and John W. Hanneken, “Time Fractional Schrodinger Equation Revisited,” Advances in Mathematical Physics, vol. 2013, pp. 1–11, 2013.
- Dexter O. Cahoy, “Some skew-symmetric distributions which include the bimodal ones,” Communications in Statistics - Theory and Methods, pp. 00–00, 2014.
- Pradeep Kumar, D. N. Pandey, and D. Bahuguna, “Approximations Of Solutions To A Retarded Type Fractional Differential Equation With A Deviated Argument,” Journal of Integral Equations and Applications, vol. 26, no. 2, pp. 215–242, 2014.
- Gianni Pagnini, “Short Note on the emergence of fractional kinetics,” Physica A: Statistical Mechanics and its Applications, 2014.
- F.F. Dou, and Y.C. Hon, “Numerical computation for backward time-fractional diffusion equation,” Engineering Analysis with Boundary Elements, vol. 40, pp. 138–146, 2014.
- Sabrina Roscani, and Eduardo Santillan Marcus, “A new equivalence of Stefan’s problems for the time fractional diffusion equation,” Fractional Calculus and Applied Analysis, vol. 17, no. 2, pp. 371–381, 2014.
- Rudolf Gorenflo, and Francesco Mainardi, “On the Fractional Poisson Process and the Discretized Stable Subordinator,” Axioms, vol. 4, no. 3, pp. 321–344, 2015.
- F. Silva Costa, J. A. P. F. Marão, J. C. Alves Soares, and E. Capelas de Oliveira, “Similarity solution to fractional nonlinear space-time diffusion-wave equation,” Journal of Mathematical Physics, vol. 56, no. 3, pp. 033507, 2015.
- André Liemert, and Alwin Kienle, “Fundamental solution of the tempered fractional diffusion equation,” Journal of Mathematical Physics, vol. 56, no. 11, pp. 113504, 2015.
- Domingo Alberto Tarzia, “Determination of One Unknown Thermal Coefficient through the One-Phase Fractional Lam&eacute;-Clapeyron-Stefan Problem,” Applied Mathematics, vol. 06, no. 13, pp. 2182–2191, 2015.
- Evangelos Bakalis, and Francesco Zerbetto, “Time Fractional Diffusion Equations and Analytical Solvable Models,” Journal of Physics: Conference Series, vol. 738, pp. 012106, 2016.
- Gianni Pagnini, and Paolo Paradisi, “A Stochastic Solution With Gaussian Stationary Increments Of The Symmetric Space-Time Fractional Diffusion Equation,” Fractional Calculus And Applied Analysis, vol. 19, no. 2, pp. 408–440, 2016.
- Abdul Shakeel, Sohail Ahmad, Hamid Khan, and Dumitru Vieru, “Solutions with Wright functions for time fractional convection flow near a heated vertical plate,” Advances in Difference Equations, vol. 2016, no. 1, 2016.
- Daniel Molina-García, Tuan Minh Pham, Paolo Paradisi, Carlo Manzo, and Gianni Pagnini, “Fractional kinetics emerging from ergodicity breaking in random media,” Physical Review E, vol. 94, no. 5, 2016.