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Physical Review E - Statistical, Nonlinear, and Soft Matter Physics, ISSN 1539-3755, 08/2009, Volume 80, Issue 2, p. 022103
Application of the fractional calculus to quantum processes is presented. In particular, the quantum dynamics is considered in the framework of the fractional... 
Brownian motion | SPACE | ANOMALOUS DIFFUSION | Schrodinger equation | PHYSICS, FLUIDS & PLASMAS | KINETICS | PROPAGATORS | quantum theory | SCHRODINGER-EQUATION | Green's function methods | PHYSICS, MATHEMATICAL
Journal Article
Physical Review E - Statistical, Nonlinear, and Soft Matter Physics, ISSN 1539-3755, 08/2015, Volume 92, Issue 2, p. 022139
A quantum-mechanical analysis of hyperfast (faster than ballistic) diffusion of a quantum wave packet in random optical lattices is presented. The main... 
PHYSICS, MATHEMATICAL | PHYSICS, FLUIDS & PLASMAS | DISORDER-ENHANCED TRANSPORT
Journal Article
Physical Review E - Statistical, Nonlinear, and Soft Matter Physics, ISSN 1539-3755, 05/2011, Volume 83, Issue 5, p. 052106
Subdiffusion on a fractal comb is considered. A mechanism of subdiffusion with a transport exponent different from 1/2 is suggested. It is shown that the... 
PHYSICS, MATHEMATICAL | RANDOM-WALKS | PHYSICS, FLUIDS & PLASMAS
Journal Article
Chaos, Solitons and Fractals, ISSN 0960-0779, 2011, Volume 44, Issue 4, pp. 348 - 352
► FTSE is insufficient to describe a quantum process. ► A quantum comb is an exact example, where the fractional time derivative is naturally introduced. ►... 
SPACE | ANOMALOUS DIFFUSION | MATHEMATICS, INTERDISCIPLINARY APPLICATIONS | PHYSICS, MULTIDISCIPLINARY | PHYSICS, MATHEMATICAL | PROPAGATORS
Journal Article
Chaos, Solitons and Fractals: the interdisciplinary journal of Nonlinear Science, and Nonequilibrium and Complex Phenomena, ISSN 0960-0779, 02/2015, Volume 71, pp. 73 - 77
•A quantum Lévy process in a box involves topological constraints in space.•The eigenvalue problem is formulated for the Lévy process in the box.•The path... 
MATHEMATICS, INTERDISCIPLINARY APPLICATIONS | DIFFUSION | PHYSICS, MULTIDISCIPLINARY | PHYSICS, MATHEMATICAL
Journal Article
Physical Review E - Statistical, Nonlinear, and Soft Matter Physics, ISSN 1539-3755, 01/2010, Volume 81, Issue 1, p. 017601
The nonlinear Schrodinger equation in the presence of disorder is considered. The dynamics of an initially localized wave packet is studied. A subdiffusive... 
ANOMALOUS DIFFUSION | CHAOS | TRANSPORT | RANDOM-WALKS | PHYSICS, FLUIDS & PLASMAS | LATTICES | ANDERSON LOCALIZATION | PHYSICS, MATHEMATICAL
Journal Article
Chaos, Solitons and Fractals: the interdisciplinary journal of Nonlinear Science, and Nonequilibrium and Complex Phenomena, ISSN 0960-0779, 02/2015, Volume 71, pp. 46 - 54
The influence of a radio-frequency electric field on glioma brain cancer development is considered. Specifically, the effectiveness of this medical technology... 
PHYSICS, MULTIDISCIPLINARY | PROLIFERATION | MODEL | PHYSICS, MATHEMATICAL | CANCER | IN-VITRO | INVASION | GLIOBLASTOMA | MATHEMATICS, INTERDISCIPLINARY APPLICATIONS | RANDOM-WALKS | CELL-MIGRATION | GROW HYPOTHESIS | TUMOR-GROWTH | Drug therapy | Gliomas | Health aspects | Analysis
Journal Article
Nonlinear Dynamics, ISSN 0924-090X, 6/2015, Volume 80, Issue 4, pp. 1853 - 1860
Fractional tumor development is considered in the framework of one-dimensional continuous time random walks (CTRW) in the presence of chemotherapy. The... 
Engineering | Vibration, Dynamical Systems, Control | Fractional transport | Migration–proliferation dichotomy | Mechanics | Automotive Engineering | Mechanical Engineering | Tumor development | MECHANICS | CELL-MIGRATION | GROWTH | PROLIFERATION | DIFFUSION | Migration-proliferation dichotomy | MODEL | DICHOTOMY | ENGINEERING, MECHANICAL
Journal Article
Physical Review E - Statistical, Nonlinear, and Soft Matter Physics, ISSN 1539-3755, 09/2012, Volume 86, Issue 3, p. 032101
A possible mechanism of superdiffusion of ultracold atoms in a one-dimensional polarization optical lattice, observed experimentally in Phys. Rev. Lett. 108,... 
FRACTIONAL KINETICS | WALKS | PHYSICS, MATHEMATICAL | PHYSICS, FLUIDS & PLASMAS
Journal Article
Chaos, Solitons and Fractals: the interdisciplinary journal of Nonlinear Science, and Nonequilibrium and Complex Phenomena, ISSN 0960-0779, 09/2018, Volume 114, pp. 551 - 555
We give exact analytical results for diffusion with a power-law position dependent diffusion coefficient along the main channel (backbone) on a comb and grid... 
Heterogeneous diffusion | Fractal grid | Comb | ANOMALOUS DIFFUSION | MATHEMATICS, INTERDISCIPLINARY APPLICATIONS | PHYSICS, MULTIDISCIPLINARY | RANDOM-WALK | MEDIA | PHYSICS, MATHEMATICAL | Physics - Statistical Mechanics
Journal Article
Physical Review E - Statistical, Nonlinear, and Soft Matter Physics, ISSN 1539-3755, 09/2009, Volume 80, Issue 3, p. 037601
The dynamics of an initially localized Anderson mode is studied in the framework of the nonlinear Schrödinger equation in the presence of disorder. It is shown... 
Scattering, Radiation | Electromagnetic Fields | Models, Statistical | Nonlinear Dynamics | Computer Simulation | Light
Journal Article
EPL, ISSN 0295-5075, 10/2018, Volume 124, Issue 2, p. 20005
A Cattaneo equation for a comb structure is considered. We present a rigorous analysis of the obtained fractional diffusion equation, and corresponding... 
ANOMALOUS DIFFUSION | TRANSPORT | MODELS | PHYSICS, MULTIDISCIPLINARY | CATTANEO | PRABHAKAR | EQUATION | PROPAGATION | Physics - Statistical Mechanics
Journal Article
Physical Review E - Statistical, Nonlinear, and Soft Matter Physics, ISSN 1539-3755, 06/2014, Volume 89, Issue 6, p. 062921
We study the phenomena of Anderson localization in the presence of nonlinear interaction on a lattice. A class of nonlinear Schrodinger models with arbitrary... 
ANOMALOUS DIFFUSION | TRANSPORT | STRANGE KINETICS | DISORDERED MEDIA | RANDOM-WALKS | PHYSICS, FLUIDS & PLASMAS | SCHRODINGER-EQUATION | BURNING PLASMAS | LEVY FLIGHTS | FRACTIONAL KINETICS | PHYSICS, MATHEMATICAL | FOKKER-PLANCK EQUATIONS | Models, Theoretical | Motion | Diffusion | Nonlinear Dynamics | Physics - Chaotic Dynamics
Journal Article
Physical Review E - Statistical, Nonlinear, and Soft Matter Physics, ISSN 1539-3755, 06/2009, Volume 79, Issue 6, p. 062102
The Lyapunov exponents for Anderson localization are studied in a one-dimensional disordered system. A random Gaussian potential with the power-law decay... 
ANOMALOUS DIFFUSION | PHYSICS, FLUIDS & PLASMAS | ANDERSON LOCALIZATION | MODEL | GUIDE | PHYSICS, MATHEMATICAL | CORRELATED DISORDER
Journal Article
Physical Review Letters, ISSN 0031-9007, 03/2007, Volume 98, Issue 11, p. 118101
We propose a two-component reaction-transport model for the migration-proliferation dichotomy in the spreading of tumor cells. By using a continuous time... 
SYSTEM | PHYSICS, MULTIDISCIPLINARY | GLIOMA GROWTH | DYNAMICS | PATTERNS | DIFFUSION | MODEL | BRAIN-TUMORS | Cell Growth Processes - physiology | Neoplasms - pathology | Models, Biological | Neoplasm Invasiveness | Cell Movement - physiology
Journal Article
Chaos, Solitons and Fractals: the interdisciplinary journal of Nonlinear Science, and Nonequilibrium and Complex Phenomena, ISSN 0960-0779, 08/2013, Volume 53, pp. 46 - 51
We suggest a modification of a comb model to describe anomalous transport in spiny dendrites. Geometry of the comb structure consisting of a one-dimensional... 
ANOMALOUS DIFFUSION | ELECTRODIFFUSION | WAVES | MATHEMATICS, INTERDISCIPLINARY APPLICATIONS | CABLE EQUATION MODELS | PHYSICS, MULTIDISCIPLINARY | DOMAIN SOLUTIONS | PHYSICS, MATHEMATICAL
Journal Article
Journal of Physics A: Mathematical and Theoretical, ISSN 1751-8113, 07/2016, Volume 49, Issue 35, p. 355001
Comb geometry, constituted of a backbone and fingers, is one of the most simple paradigm of a two-dimensional structure, where anomalous diffusion can be... 
fractal dimension | fractional derivatives | anomalous diffusion | fractal comb | Lévy processes | MODELS | PHYSICS, MULTIDISCIPLINARY | RANDOM-WALKS | Levy processes | EQUATIONS | PHYSICS, MATHEMATICAL | FRACTIONAL DIFFUSION
Journal Article
Physical Review E - Statistical, Nonlinear, and Soft Matter Physics, ISSN 1539-3755, 03/2015, Volume 91, Issue 3, p. 032108
A grid comb model is a generalization of the well known comb model, and it consists of N backbones. For N = 1 the system reduces to the comb model where... 
TRANSPORT | MODELS | PHYSICS, MATHEMATICAL | PHYSICS, FLUIDS & PLASMAS | RANDOM-WALK | Physics - Statistical Mechanics
Journal Article
Physical Review E - Statistical, Nonlinear, and Soft Matter Physics, ISSN 1539-3755, 03/2007, Volume 75, Issue 3, p. 037201
It is shown that the Weyl fractional derivative can quantize an open system. A fractional kicked rotor is studied in the framework of the fractional... 
SYSTEMS | PHASE-SPACE | QUANTUM-MECHANICS | PHYSICS, MATHEMATICAL | PHYSICS, FLUIDS & PLASMAS | KINETICS | Physics - Chaotic Dynamics
Journal Article
Chaos, Solitons and Fractals, ISSN 0960-0779, 2011, Volume 44, Issue 4, pp. 335 - 341
► The electric field in a composite dielectric with a fractal charge distribution is observed. ► The observation is based on a relation between fractal... 
DYNAMICS | MATHEMATICS, INTERDISCIPLINARY APPLICATIONS | PHYSICS, MULTIDISCIPLINARY | PHYSICS, MATHEMATICAL | RANDOM-WALK
Journal Article
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