Fractional dynamics of systems with long-range interaction

[1]  E. Lieb,et al.  Phase transitions and reflection positivity. I. General theory and long range lattice models , 1978 .

[2]  S. Flach Breathers on lattices with long range interaction , 1998, cond-mat/9809387.

[3]  Freeman J. Dyson,et al.  Existence of a phase-transition in a one-dimensional Ising ferromagnet , 1969 .

[4]  Robert S. MacKay,et al.  Proof of existence of breathers for time-reversible or Hamiltonian networks of weakly coupled oscillators , 1994 .

[5]  Nick Laskin,et al.  Fractals and quantum mechanics. , 2000, Chaos.

[6]  R. Nigmatullin The Realization of the Generalized Transfer Equation in a Medium with Fractal Geometry , 1986, January 1.

[7]  J. Rogers Chaos , 1876, Molecular Vibrations.

[8]  Vladimir V. Uchaikin,et al.  Anomalous diffusion and fractional stable distributions , 2003 .

[9]  Alain Pumir,et al.  Anomalous diffusion of tracer in convection rolls , 1989 .

[10]  V. E. Tarasov Fractional hydrodynamic equations for fractal media , 2005, physics/0602096.

[11]  Vladimir V. Uchaikin,et al.  REVIEWS OF TOPICAL PROBLEMS: Self-similar anomalous diffusion and Levy-stable laws , 2003 .

[12]  J. Klafter,et al.  The random walk's guide to anomalous diffusion: a fractional dynamics approach , 2000 .

[13]  Arkady Pikovsky,et al.  A universal concept in nonlinear sciences , 2006 .

[14]  Yoshiki Kuramoto,et al.  Rotating spiral waves with phase-randomized core in nonlocally coupled oscillators. , 2003, Physical review. E, Statistical, nonlinear, and soft matter physics.

[15]  Sergei F. Mingaleev,et al.  Effects of nonlocal dispersive interactions on self-trapping excitations , 1997 .

[16]  Vickie E. Lynch,et al.  Anomalous diffusion and exit time distribution of particle tracers in plasma turbulence model , 2001 .

[17]  Freeman J. Dyson,et al.  An Ising ferromagnet with discontinuous long-range order , 1971 .

[18]  V S Afraimovich,et al.  Multivalued mappings in generalized chaos synchronization. , 2001, Physical review. E, Statistical, nonlinear, and soft matter physics.

[19]  S. Boccaletti,et al.  Synchronization of chaotic systems , 2001 .

[20]  Minoru Takahashi,et al.  Quantum Heisenberg Chain with Long-Range Ferromagnetic Interactions at Low Temperatures , 1994 .

[21]  R. Hilfer Applications Of Fractional Calculus In Physics , 2000 .

[22]  Alexander I. Saichev,et al.  Fractional kinetic equations: solutions and applications. , 1997, Chaos.

[23]  H. Jürgensen Synchronization , 2021, Inf. Comput..

[24]  Alexander S. Mikhailov,et al.  Birhythmicity, synchronization, and turbulence in an oscillatory system with nonlocal inertial coupling , 2005, nlin/0502015.

[25]  Department of Physics,et al.  Some Applications of Fractional Equations , 2003 .

[26]  Feller William,et al.  An Introduction To Probability Theory And Its Applications , 1950 .

[27]  Jürgen Kurths,et al.  Synchronization - A Universal Concept in Nonlinear Sciences , 2001, Cambridge Nonlinear Science Series.

[28]  J. Krisch Fractional boundary for the Gott-Hiscock string , 2005 .

[29]  Nakano,et al.  Quantum Heisenberg model with long-range ferromagnetic interactions. , 1993, Physical review. B, Condensed matter.

[30]  Vasily E. Tarasov,et al.  Electromagnetic field of fractal distribution of charged particles , 2005, physics/0610010.

[31]  Andrew J. Majda,et al.  A one-dimensional model for dispersive wave turbulence , 1997 .

[32]  G. Uhlenbeck,et al.  Studies in statistical mechanics , 1962 .

[33]  A. Erdélyi,et al.  Higher Transcendental Functions , 1954 .

[34]  Vasily E. Tarasov Possible experimental test of continuous medium model for fractal media , 2005 .

[35]  V. E. Tarasov Continuous Medium Model for Fractal Media , 2005, cond-mat/0506137.

[36]  O. Marichev,et al.  Fractional Integrals and Derivatives: Theory and Applications , 1993 .

[37]  Francesco Mainardi,et al.  On Mittag-Leffler-type functions in fractional evolution processes , 2000 .

[38]  G. G. Stokes "J." , 1890, The New Yale Book of Quotations.

[39]  G. Zaslavsky,et al.  Nonlinear fractional dynamics on a lattice with long range interactions , 2005, nlin/0512010.

[40]  T. MacRobert Higher Transcendental Functions , 1955, Nature.

[41]  D. Benson,et al.  Operator Lévy motion and multiscaling anomalous diffusion. , 2001, Physical review. E, Statistical, nonlinear, and soft matter physics.

[42]  N. Laskin Fractional Schrödinger equation. , 2002, Physical review. E, Statistical, nonlinear, and soft matter physics.

[43]  M. Naber Time fractional Schrödinger equation , 2004, math-ph/0410028.

[44]  C. R. Willis,et al.  Discrete Breathers , 1997 .

[45]  Nakano,et al.  Magnetic properties of quantum Heisenberg ferromagnets with long-range interactions. , 1995, Physical review. B, Condensed matter.

[46]  Valentin Afraimovich,et al.  Synchronization in directionally coupled systems: Some rigorous results , 2001 .

[47]  R. Gorenflo,et al.  Wright functions as scale-invariant solutions of the diffusion-wave equation , 2000 .

[48]  Monika Sharma,et al.  Chemical oscillations , 2006 .

[49]  George M. Zaslavsky,et al.  Fractional kinetics: from pseudochaotic dynamics to Maxwell’s Demon , 2004 .

[50]  Andrew G. Glen,et al.  APPL , 2001 .

[51]  A. Winfree Biological rhythms and the behavior of populations of coupled oscillators. , 1967, Journal of theoretical biology.

[52]  N. Laskin Fractional quantum mechanics and Lévy path integrals , 1999, hep-ph/9910419.

[53]  J. Sousa Phase diagram in the quantum XY model with long-range interactions , 2005 .

[54]  J. Rasmussen,et al.  Fractional generalization of the Ginzburg–Landau equation: an unconventional approach to critical phenomena in complex media , 2003, cond-mat/0309577.

[55]  G. Zaslavsky Chaos, fractional kinetics, and anomalous transport , 2002 .

[56]  V. E. Tarasov,et al.  Fractional Fokker-Planck equation for fractal media. , 2005, Chaos.

[57]  G. Zaslavsky,et al.  Fractional Ginzburg–Landau equation for fractal media , 2005, physics/0511144.

[58]  R. MacKay,et al.  ALGEBRAIC LOCALISATION OF LINEAR RESPONSE IN NETWORKS WITH ALGEBRAICALLY DECAYING INTERACTION, AND APPLICATION TO DISCRETE BREATHERS IN DIPOLE-DIPOLE SYSTEMS , 1999 .

[59]  N F Rulkov,et al.  Generalized synchronization of chaos in noninvertible maps. , 2002, Physical review. E, Statistical, nonlinear, and soft matter physics.

[60]  F. Dyson Non-existence of spontaneous magnetization in a one-dimensional Ising ferromagnet , 1969 .

[61]  S. Aubry,et al.  Breathers in nonlinear lattices: existence, linear stability and quantization , 1997 .

[62]  Yoshiki Kuramoto,et al.  Chemical Oscillations, Waves, and Turbulence , 1984, Springer Series in Synergetics.

[63]  Yuri S. Kivshar,et al.  Nonlinear dynamics of the Frenkel—Kontorova model , 1998 .

[64]  George M. Zaslavsky,et al.  Fractional kinetic equation for Hamiltonian chaos , 1994 .

[65]  Raoul R. Nigmatullin,et al.  Fractional integral and its physical interpretation , 1992 .

[66]  Y. Kuramoto,et al.  Complex Ginzburg-Landau equation with nonlocal coupling. , 2003, Physical review. E, Statistical, nonlinear, and soft matter physics.

[67]  D. Benson,et al.  Multidimensional advection and fractional dispersion. , 1999, Physical review. E, Statistical physics, plasmas, fluids, and related interdisciplinary topics.