The fractional Boltzmann transport equation
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[1] John B. Shoven,et al. I , Edinburgh Medical and Surgical Journal.
[2] Delfim F. M. Torres,et al. Constants of motion for fractional action-like variational problems , 2006, math/0607472.
[3] J. A. Tenreiro Machado,et al. Special Issue on “Discontinuous and Fractional Dynamical Systems” , 2008 .
[4] Fractional dynamic symmetries and the ground state properties of nuclei , 2008, 0806.2300.
[5] R. Herrmann. Higher-dimensional mixed fractional rotation groups as a basis for dynamic symmetries generating the spectrum of the deformed Nilsson oscillator , 2010 .
[6] O. Marichev,et al. Fractional Integrals and Derivatives: Theory and Applications , 1993 .
[7] El-nabulsi Ahmad Rami. Fractional dynamics, fractional weak bosons masses and physics beyond the standard model , 2009 .
[8] R A El Nabulsi,et al. A FRACTIONAL ACTION-LIKE VARIATIONAL APPROACH OF SOME CLASSICAL, QUANTUM AND GEOMETRICAL DYNAMICS , 2005 .
[9] R. Sibatov,et al. Fractional differential kinetics of charge transport in unordered semiconductors , 2007 .
[10] J. Klafter,et al. The random walk's guide to anomalous diffusion: a fractional dynamics approach , 2000 .
[11] Carl F. Lorenzo,et al. Fractional Trigonometry and the Spiral Functions , 2004 .
[12] The fractional symmetric rigid rotor , 2006, nucl-th/0610091.
[13] Claude Garrod,et al. Statistical mechanics and thermodynamics , 1995 .
[14] V. E. Tarasov. Fractional Vector Calculus and Fractional Maxwell's Equations , 2008, 0907.2363.
[15] J. Bouchaud,et al. Anomalous diffusion in disordered media: Statistical mechanisms, models and physical applications , 1990 .
[16] G. Kalman. Strongly Coupled Coulomb Systems , 2013 .
[17] Fractional Boltzmann equation for resonance radiation transport in plasma , 2010, 1008.4439.
[18] H. Srivastava,et al. Theory and Applications of Fractional Differential Equations , 2006 .
[19] Malgorzata Klimek,et al. Lagrangean and Hamiltonian fractional sequential mechanics , 2002 .
[20] Denis Serre,et al. Handbook of mathematical fluid dynamics , 2002 .
[21] Rami Ahmad El-Nabulsi,et al. Universal fractional Euler-Lagrange equation from a generalized fractional derivate operator , 2011 .
[22] Riewe,et al. Nonconservative Lagrangian and Hamiltonian mechanics. , 1996, Physical review. E, Statistical physics, plasmas, fluids, and related interdisciplinary topics.
[23] O. Agrawal,et al. Advances in Fractional Calculus: Theoretical Developments and Applications in Physics and Engineering , 2007 .
[24] V. Zolotarev,et al. Superdiffusion and stable laws , 1999 .
[25] V. E. Tarasov. Fractional variations for dynamical systems: Hamilton and Lagrange approaches , 2006, math-ph/0606048.
[26] ENTROPY PRODUCTION AND CONVERGENCE TO EQUILIBRIUM FOR THE BOLTZMANN EQUATION , 2006 .
[27] N. Laskin,et al. Fractional quantum mechanics , 2008, Physical review. E, Statistical physics, plasmas, fluids, and related interdisciplinary topics.
[28] K. Tas,et al. Fractional hamiltonian analysis of higher order derivatives systems , 2006, math-ph/0612024.
[29] Mohamed A. E. Herzallah,et al. Fractional-order Euler–Lagrange equations and formulation of Hamiltonian equations , 2009 .
[30] Jacky Cresson,et al. Fractional embedding of differential operators and Lagrangian systems , 2006, math/0605752.
[31] A. R. El-Nabulsi. FRACTIONAL QUANTUM EULER–CAUCHY EQUATION IN THE SCHRÖDINGER PICTURE, COMPLEXIFIED HARMONIC OSCILLATORS AND EMERGENCE OF COMPLEXIFIED LAGRANGIAN AND HAMILTONIAN DYNAMICS , 2009 .
[32] G. Zaslavsky. Chaos, fractional kinetics, and anomalous transport , 2002 .
[33] Investigation of apparent violation of the second law of thermodynamics in quantum transport studies , 2002, cond-mat/0204302.
[34] Frederick E. Riewe,et al. Mechanics with fractional derivatives , 1997 .
[35] F. Mainardi,et al. Fractals and fractional calculus in continuum mechanics , 1997 .
[36] Ervin Goldfain,et al. Complexity in quantum field theory and physics beyond the standard model , 2005 .
[37] François Golse,et al. Kinetic equations and asympotic theory , 2000 .
[38] A. Raspini. Simple Solutions of the Fractional Dirac Equation of Order 2/3 , 2001 .
[39] Dumitru Baleanu,et al. Hamiltonian formulation of systems with linear velocities within Riemann–Liouville fractional derivatives , 2005 .
[40] Rami Ahmad El-Nabulsi,et al. FRACTIONAL FIELD THEORIES FROM MULTI-DIMENSIONAL FRACTIONAL VARIATIONAL PROBLEMS , 2008 .
[41] Om P. Agrawal,et al. Fractional variational calculus and the transversality conditions , 2006 .
[42] I. Sokolov,et al. Anomalous transport : foundations and applications , 2008 .
[43] Cédric Villani,et al. On the trend to global equilibrium for spatially inhomogeneous kinetic systems: The Boltzmann equation , 2005 .
[44] Delfim F. M. Torres,et al. A formulation of Noether's theorem for fractional problems of the calculus of variations , 2007 .
[45] Delfim F. M. Torres,et al. Necessary optimality conditions for fractional action-like integrals of variational calculus with Riemann-Liouville derivatives of order (α, β) , 2007 .
[46] R. Nabulsi,et al. A FRACTIONAL APPROACH TO NON-CONSERVATIVE LAGRANGIAN DYNAMICAL SYSTEMS , 2005 .
[47] R. Hilfer. Applications Of Fractional Calculus In Physics , 2000 .
[48] T. Pritz,et al. ANALYSIS OF FOUR-PARAMETER FRACTIONAL DERIVATIVE MODEL OF REAL SOLID MATERIALS , 1996 .
[49] O. Agrawal,et al. Fractional hamilton formalism within caputo’s derivative , 2006, math-ph/0612025.
[50] Vasily E. Tarasov,et al. Fokker–Planck equation with fractional coordinate derivatives , 2008, 0805.0606.
[51] José António Tenreiro Machado,et al. Fractional calculus applications in signals and systems , 2006, Signal Processing.
[52] R. Bagley,et al. On the Fractional Calculus Model of Viscoelastic Behavior , 1986 .
[53] C. Cercignani. The Boltzmann equation and its applications , 1988 .
[54] Delfim F. M. Torres,et al. Fractional conservation laws in optimal control theory , 2007, 0711.0609.
[55] Om P. Agrawal,et al. Formulation of Euler–Lagrange equations for fractional variational problems , 2002 .
[56] Igor M. Sokolov,et al. Physics of Fractal Operators , 2003 .
[57] D. Villamaina,et al. On anomalous diffusion and the out of equilibrium response function in one-dimensional models , 2011, 1101.4097.
[58] Dumitru Baleanu,et al. Fractional Nambu Mechanics , 2009 .
[59] K. B. Oldham,et al. The Fractional Calculus: Theory and Applications of Differentiation and Integration to Arbitrary Order , 1974 .
[60] J. Craggs. Applied Mathematical Sciences , 1973 .
[61] R. Illner,et al. The mathematical theory of dilute gases , 1994 .
[62] J. Klafter,et al. Anomalous Diffusion and Relaxation Close to Thermal Equilibrium: A Fractional Fokker-Planck Equation Approach , 1999 .
[63] Delfim F. M. Torres,et al. Fractional actionlike variational problems , 2008, 0804.4500.
[64] SUBDIFFUSION OVER FRACTIONAL QUANTUM PATHS WITHOUT FRACTIONAL DERIVATIVE , 2008 .
[65] C. Villani. Chapter 2 – A Review of Mathematical Topics in Collisional Kinetic Theory , 2002 .
[66] Teodor M. Atanackovic,et al. An Expansion Formula for Fractional Derivatives and its Application , 2004 .
[67] V. E. Tarasov. Fractional generalization of gradient and hamiltonian systems , 2005, math/0602208.
[68] REVIEWS OF TOPICAL PROBLEMS: Fractional differential approach to dispersive transport in semiconductors , 2009 .
[69] R. El-Nabulsi. MODIFICATIONS AT LARGE DISTANCES FROM FRACTIONAL AND FRACTAL ARGUMENTS , 2010 .
[70] Radu Balescu,et al. Statistical dynamics: matter out of equilibrium , 1997 .
[71] I. Podlubny. Fractional differential equations , 1998 .
[72] J. Rogers. Chaos , 1876 .
[73] José António Tenreiro Machado,et al. Fractional differentiation and its applications I , 2013, Comput. Math. Appl..
[74] Fractional Poisson Bracket , 2008, 0807.4255.
[75] N. Laskin. Fractional Schrödinger equation. , 2002, Physical review. E, Statistical, nonlinear, and soft matter physics.
[76] El-nabulsi Ahmad Rami. On the fractional minimal length Heisenberg–Weyl uncertainty relation from fractional Riccati generalized momentum operator , 2009 .
[77] J. A. Tenreiro Machado,et al. New Trends in Nanotechnology and Fractional Calculus Applications , 2010 .
[78] D.Baleanu,et al. Lagrangian formulation of classical fields within Riemann-Liouville fractional derivatives , 2005, hep-th/0510071.
[79] R. Gorenflo,et al. Fractional Calculus: Integral and Differential Equations of Fractional Order , 2008, 0805.3823.
[80] R. Gorenflo,et al. AN OPERATIONAL METHOD FOR SOLVING FRACTIONAL DIFFERENTIAL EQUATIONS WITH THE CAPUTO DERIVATIVES , 1999 .
[81] Malgorzata Klimek,et al. Fractional sequential mechanics — models with symmetric fractional derivative , 2001 .
[82] V. Uchaikin. Subdiffusion and stable laws , 1999 .
[83] A. R. El-Nabulsi. THE FRACTIONAL CALCULUS OF VARIATIONS FROM EXTENDED ERDÉLYI-KOBER OPERATOR , 2009 .
[84] E. T. Jaynes,et al. Violation of Boltzmann's H Theorem in Real Gases , 1971 .
[85] O. Agrawal,et al. A Numerical Scheme for Dynamic Systems Containing Fractional Derivatives , 2002 .
[86] Debra J Searles,et al. Experimental demonstration of violations of the second law of thermodynamics for small systems and short time scales. , 2002, Physical review letters.
[87] George M. Zaslavsky. Hamiltonian Chaos and Fractional Dynamics , 2005 .
[88] Ravi P. Agarwal,et al. Existence of fractional neutral functional differential equations , 2010, Comput. Math. Appl..