The continuous time random walk, still trendy: fifty-year history, state of art and outlook, Eur. Phys. J. B, vol.90, p.50, 2017. ,
, The asymptotic universality of the Mittag-Leffler waiting time law in continuous time random walks, Invited lecture at the 373. WE-Heraeus-Seminar on Anomalous Transport: Experimental Results and Theoretical Challenges, pp.12-16, 2006.
, Mittag-Leffler Waiting Time, Power Laws, Rarefaction, Continuous Time Random Walk, Diffusion Limit, 2010.
The Random Walk's Guide to Anomalous Diffusion : A Fractional Dynamics Approach, Phys. Rep, vol.339, pp.1-77, 2000. ,
The restaurant at the end of the random walk: recent developments in the description of anomalous transport by fractional dynamics, J. Phys. A: Math. Gen, vol.37, pp.161-208, 2004. ,
Chaos, fractional kinetics, and anomalous transport, Phys. Rep, vol.371, issue.6, pp.461-580, 2002. ,
Fractional kinetic equations: solutions and applications, Chaos, vol.7, p.753, 1997. ,
Models based on Mittag-Leffler functions for anomalous relaxation in dielectrics, The European Physical Journal, Special Topics, vol.193, pp.161-171, 2011. ,
Creep, relaxation and viscosity properties for basic fractional models in rheology, The European Physical Journal, Special Topics, vol.193, pp.133-160, 2011. ,
Fractional relaxation of distributed order, Complexus Mundi: Emergent Patterns in Nature (M. Novak Ed.), pp.33-42, 2006. ,
Random walks on lattices II, J. Math. Phys, vol.6, issue.2, pp.167-181, 1965. ,
Fractional master equations and fractal time random walks, Phys. Rev. E, vol.51, issue.2, p.848, 1995. ,
The Fractional Poisson Process and the Inverse Stable Subordinator, Electron. J. Probab, vol.16, issue.59, pp.1600-1620, 2011. ,
What is a fractional derivative?, Journal of Computational Physics, vol.293, pp.4-13, 2015. ,
No fractional derivative, Communications in Nonlinear Science and Numerical Simulation, vol.62, pp.157-163, 2018. ,
A comment on some new definitions of fractional derivative, Nonlinear Dynamics, vol.93, pp.1757-1763, 2018. ,
, Desiderata for fractional derivatives and integrals, vol.7, p.149, 2019.
Hilfer-Prabhakar derivatives and some applications, Appl. Math. Comput, vol.242, pp.576-589, 2014. ,
On complete monotonicity of the Prabhakar function and non-Debye relaxation in dielectrics, Journal of Computational Physics, vol.293, pp.70-80, 2015. ,
A practical guide to Prabhakar fractional calculus, Fract. Calc. Appl. Anal, vol.23, issue.1, pp.9-54, 2020. ,
A singular integral equation with a generalized Mittag-Leffler function in the kernel, Yokohama Math. J, vol.19, pp.7-15, 1971. ,
Renewal processes based on generalized Mittag-Leffler waiting times, Commun Nonlinear Sci Numer Simul, vol.18, issue.3, pp.639-650, 2013. ,
Continuous time random walk and diffusion with generalized fractional Poisson process, Physica A: Statistical Mechanics and its Applications, vol.545, 2020. ,
URL : https://hal.archives-ouvertes.fr/hal-02336450
Generalized fractional Poisson process and related stochastic dynamics, Fractional Calculus & Applied Analysis, vol.23, issue.3, pp.656-693, 2020. ,
URL : https://hal.archives-ouvertes.fr/hal-02888237
Generalized space-time fractional dynamics in networks and lattices Generalized Space-Time Fractional Dynamics in Networks and Lattices, Nonlinear Wave Dynamics of Materials and Structures, vol.122, 2020. ,
URL : https://hal.archives-ouvertes.fr/hal-02314815
On Discrete-Time Generalized Fractional Poisson Process And Related Stochastic Dynamics ,
General fractional calculus, evolution equations, and renewal processes, Integral Equations and Operator Theory, vol.71, pp.583-600, 2011. ,
, Networks: An Introduction, 2010.
Random walks on complex networks, Phys. Rev. Lett, vol.92, p.118701, 2004. ,
, Random Walks and Random Environments, Vols. 1, 1995.
Random Walks and Random Environments, 1996. ,
, Graph Theory, Combinatorics, and Applications, vol.2, p.871, 1991.
, Graph Symmetry: Algebraic Methods and Applications, vol.497, p.227, 1997.
, Fractional Dynamics on Networks and Lattices, p.9781786301581, 2019.
Fractional dynamics on networks: Emergence of anomalous diffusion and Lévy flights, Phys. Rev. E, vol.90, p.32809, 2014. ,
Random walks on networks with stochastic resetting, Phys. Rev. E, vol.101, p.62147, 2020. ,
Networks and long-range mobility in cities: A study of more than one billion taxi trips, Scientific Reports, vol.10, p.4022, 2020. ,
Random walks with long-range steps generated by functions of Laplacian matrices, J. Stat. Mech, p.43404, 2018. ,
URL : https://hal.archives-ouvertes.fr/hal-02315587
Non-local biased random walks and fractional transport on directed networks, Phys. Rev. E, vol.102, p.22142, 2020. ,
URL : https://hal.archives-ouvertes.fr/hal-02540672
, On the Fractional Poisson Process and the Discretized Stable Subordinator, vol.4, pp.321-344, 2015.
, On Discrete-Time Semi-Markov processes, Discrete and Continuous Dynamical Systems B (2020)
The space-fractional Poisson process, Statistics & Probability Letters, vol.82, issue.4, pp.852-858, 2012. ,
, , p.218, 1973.
, Renewal Theory, 1967.
A generalization of the space-fractional Poisson process and its connection to some Lévy processes, Electron. Commun. Probab, vol.21, issue.20, pp.1-14, 2016. ,
The Laplace transform, 1941. ,
, Bernstein functions. Theory and applications, vol.37, 2012.
, Über Matrizen aus nicht negativen Elementen, Sitzungsberichte der Königlich Preussischen Akademie der Wissenschaften, pp.456-477, 1912.
Nonlocal network dynamics via fractional graph Laplacians, Journal of Complex Networks, pp.1-27, 2020. ,
Discrete Mittag-Leffler distributions, Stat. Prob. Lett, vol.23, pp.271-274, 1995. ,
Fractional Poisson law, Radiophysics and Quantum Electronics, vol.43, pp.738-741, 2000. ,
Fractional Poisson process, Communications in Nonlinear Science and Numerical Simulation, vol.8, pp.201-213, 2003. ,
A fractional generalization of the Poisson processes, Vietnam Journ. Math, vol.32, 2004. ,
Fractional Poisson processes and related planar random motions, Electron. J. Probab, vol.14, issue.61, pp.1790-1826, 2009. ,
, Fractional Integrals and Derivatives: Theory and Applications, 1993.
Counting processes with Bern?tein intertimes and random jumps, J. Appl. Probab, vol.52, issue.4, pp.1028-1044, 2015. ,
Some probabilistic properties of fractional point processes, Stoch. Anal. Appl, vol.35, issue.4, pp.701-718, 2017. ,
, Fractional Differential Equations, 1999.
Sur une généralisation de l'opérateur fractionnaire, 2011. ,
General fractional calculus and Prabhakar's theory, Commun. Nonlinear Sci. Numer. Simul, vol.83, 2020. ,
Aging in transport processes on networks with stochastic cumulative damage, Phys. Rev. E, vol.100, p.22312, 2019. ,
URL : https://hal.archives-ouvertes.fr/hal-02315117
Generalized Functions, 1968. ,
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