FDA Express    Vol. 6, No. 3, Feb. 15, 2013

Editors: http://em.hhu.edu.cn/fda/Editors.htm

Institute of Soft Matter Mechanics, Hohai University
For contribution: fdaexpress@163.com, hushuaihhu@gmail.com
For subscription: http://em.hhu.edu.cn/fda/subscription.htm

◆  Call for Paper

Special Issue on "Advanced Topics in Fractional Dynamics" in the journal "Advances in Mathematical Physics"

◆  Books

Fractional Kinetics in Solids: Anomalous Charge Transport in Semiconductors, Dielectrics and Nanosystems

◆  Journals

Nonlinear Dynamics

Journal of Computational Physics

International Journal of Mathematics & Computation

◆  Paper Highlight
State transition of a non-Ohmic damping system in a corrugated plane
Anomalous diffusion: nonlinear fractional Fokker-Planck equation

◆  Websites of Interest

Fractional Calculus & Applied Analysis, Volume 16, No 1, 2013

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Call for Paper

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Special Issue on "Advanced Topics in Fractional Dynamics" in the journal "Advances in Mathematical Physics"

(Contributed by Prof. J. A. Tenreiro Machado)
http://www.hindawi.com/journals/amp/si/372436/cfp/

Call for Papers
Fractional order differentiation consists in the generalisation of classical integer differentiation to real or complex orders. During the last decades, fractional differentiation has drawn increasing attention in the study of the so-called anomalous social and physical behaviors, where scaling power law of fractional order appears universal as an empirical description of such complex phenomena. The goal of this special issue is to address the latest developments in the area of fractional calculus application in dynamical systems. Papers describing original research work that reflects the recent theoretical advances and experimental results as well as new topics for research are invited on all aspects of object tracking. Potential topics include, but are not limited to:
Modeling and applications of complex systems in physics, biology,
biophysics, and medicine
Fractional variational principles
Continuous time random walk
Computational fractional derivative equations
Viscoelasticity
Fractional differential equations
Fractional operators on fractals
Local fractional derivatives
Automatic control Thermal systems
Electromagnetism
Economical and financial systems
Electrical, mechanical, and thermal systems
Bifurcation
Chaos
Synchronization

Before submission authors should carefully read over the journal's Author Guidelines, which are located at http://www.hindawi.com/journals/amp/guidelines/. Prospective authors should submit an electronic copy of their complete manuscript through the journal Manuscript Tracking System at http://mts.hindawi.com/submit/journals/amp/fract/ according to the following timetable:
Manuscript Due Friday, 17 May 2013
First Round of Reviews Friday, 9 August 2013
Publication Date Friday, 4 October 2013

Lead Guest Editor
Dumitru Baleanu, Department of Mathematics and Computer Sciences, Cankaya University, Ankara, Turkey

Guest Editors
H. M. Srivastava, Department of Mathematics and Statistics, University of Victoria, Victoria, BC, Canada V8W 3R4 Varsha Daftardar-Gejji, Department of Mathematics, University of Pune, Pune 411007, India
Changpin Li, Department of Mathematics, Shanghai University, Shanghai 200444, China
J. A. Tenreiro Machado, Department of Electrical Engineering, Institute of Engineering of Polytechnic of Porto, Rua Dr. Antonio Bernardino de Almeida 431, 4200-072 Porto, Portugal

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Fractional Kinetics in Solids: Anomalous Charge Transport in Semiconductors, Dielectrics and Nanosystems

Vladimir Uchaikin (Author), Renat Sibatov (Author)

Book Description
The standard (Markovian) transport model based on the Boltzmann equation cannot describe some non-equilibrium processes called anomalous that take place in many disordered solids. Causes of anomality lie in non-uniformly scaled (fractal) spatial heterogeneities, in which particle trajectories take cluster form. Furthermore, particles can be located in some domains of small sizes (traps) for a long time. Estimations show that path length and waiting time distributions are often characterized by heavy tails of the power law type. This behavior allows the introduction of time and space derivatives of fractional orders. Distinction of path length distribution from exponential is interpreted as a consequence of media fractality, and analogous property of waiting time distribution as a presence of memory. In this book, a novel approach using equations with derivatives of fractional orders is applied to describe anomalous transport and relaxation in disordered semiconductors, dielectrics and quantum dot systems. A relationship between the self-similarity of transport, the Levy stable limiting distributions and the kinetic equations with fractional derivatives is established. It is shown that unlike the well-known Scher-Montroll and Arkhipov-Rudenko models, which are in a sense alternatives to the normal transport model, fractional differential equations provide a unified mathematical framework for describing normal and dispersive transport. The fractional differential formalism allows the equations of bipolar transport to be written down and transport in distributed dispersion systems to be described. The relationship between fractional transport equations and the generalized limit theorem reveals the probabilistic aspects of the phenomenon in which a dispersive to Gaussian transport transition occurs in a time-of-flight experiment as the applied voltage is decreased and/or the sample thickness increased. Recent experiments devoted to studies of transport in quantum dot arrays are discussed in the framework of dispersive transport models. The memory phenomena in systems under consideration are discussed in the analysis of fractional equations. It is shown that the approach based on the anomalous transport models and the fractional kinetic equations may be very useful in some problems that involve nano-sized systems. These are photon counting statistics of blinking single quantum dot fluorescence, relaxation of current in colloidal quantum dot arrays, and some others.
Contents:
• Statistical Grounds
• Fractional Kinetics of Dispersive Transport
• Transient Processes in Disordered Semiconductor Structures
• Fractional Kinetics in Quantum Dots and Wires
• Fractional Relaxation in Dielectrics
• The Scale Correspondence Principle
Readership: Students and post-graduate students, engineers, applied mathematicians, material scientists and physicists, specialists in theory of solids, in mathematical modeling and numerical simulations of complex physical processes, and to all who wish to make themselves more familiar with fractional differentiation method.

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