Author: Vasily E. Tarasov
Publisher: Springer Science & Business Media
Release Date: 2011-01-04
"Fractional Dynamics: Applications of Fractional Calculus to Dynamics of Particles, Fields and Media" presents applications of fractional calculus, integral and differential equations of non-integer orders in describing systems with long-time memory, non-local spatial and fractal properties. Mathematical models of fractal media and distributions, generalized dynamical systems and discrete maps, non-local statistical mechanics and kinetics, dynamics of open quantum systems, the hydrodynamics and electrodynamics of complex media with non-local properties and memory are considered. This book is intended to meet the needs of scientists and graduate students in physics, mechanics and applied mathematics who are interested in electrodynamics, statistical and condensed matter physics, quantum dynamics, complex media theories and kinetics, discrete maps and lattice models, and nonlinear dynamics and chaos. Dr. Vasily E. Tarasov is a Senior Research Associate at Nuclear Physics Institute of Moscow State University and an Associate Professor at Applied Mathematics and Physics Department of Moscow Aviation Institute.
Author: Alexandre Almeida
Publisher: Springer Science & Business Media
Release Date: 2013-01-31
This volume is dedicated to Professor Stefan Samko on the occasion of his seventieth birthday. The contributions display the range of his scientific interests in harmonic analysis and operator theory. Particular attention is paid to fractional integrals and derivatives, singular, hypersingular and potential operators in variable exponent spaces, pseudodifferential operators in various modern function and distribution spaces, as well as related applications, to mention but a few. Most contributions were firstly presented in two conferences at Lisbon and Aveiro, Portugal, in June‒July 2011.
This book offers a comprehensive treatment of the theory of measures of noncompactness. It discusses various applications of the theory of measures of noncompactness, in particular, by addressing the results and methods of fixed-point theory. The concept of a measure of noncompactness is very useful for the mathematical community working in nonlinear analysis. Both these theories are especially useful in investigations connected with differential equations, integral equations, functional integral equations and optimization theory. Thus, one of the book’s central goals is to collect and present sufficient conditions for the solvability of such equations. The results are established in miscellaneous function spaces, and particular attention is paid to fractional calculus.
Author: Xiao Jun Yang
Publisher: Academic Press
Release Date: 2015-10-22
Local Fractional Integral Transforms and Their Applications provides information on how local fractional calculus has been successfully applied to describe the numerous widespread real-world phenomena in the fields of physical sciences and engineering sciences that involve non-differentiable behaviors. The methods of integral transforms via local fractional calculus have been used to solve various local fractional ordinary and local fractional partial differential equations and also to figure out the presence of the fractal phenomenon. The book presents the basics of the local fractional derivative operators and investigates some new results in the area of local integral transforms. Provides applications of local fractional Fourier Series Discusses definitions for local fractional Laplace transforms Explains local fractional Laplace transforms coupled with analytical methods
This book addresses the topic of fractional-order modeling of nuclear reactors. Approaching neutron transport in the reactor core as anomalous diffusion, specifically subdiffusion, it starts with the development of fractional-order neutron telegraph equations. Using a systematic approach, the book then examines the development and analysis of various fractional-order models representing nuclear reactor dynamics, ultimately leading to the fractional-order linear and nonlinear control-oriented models. The book utilizes the mathematical tool of fractional calculus, the calculus of derivatives and integrals with arbitrary non-integer orders (real or complex), which has recently been found to provide a more compact and realistic representation to the dynamics of diverse physical systems. Including extensive simulation results and discussing important issues related to the fractional-order modeling of nuclear reactors, the book offers a valuable resource for students and researchers working in the areas of fractional-order modeling and control and nuclear reactor modeling.
Author: J. Sabatier
Publisher: Springer Science & Business Media
Release Date: 2007-07-28
In the last two decades, fractional (or non integer) differentiation has played a very important role in various fields such as mechanics, electricity, chemistry, biology, economics, control theory and signal and image processing. For example, in the last three fields, some important considerations such as modelling, curve fitting, filtering, pattern recognition, edge detection, identification, stability, controllability, observability and robustness are now linked to long-range dependence phenomena. Similar progress has been made in other fields listed here. The scope of the book is thus to present the state of the art in the study of fractional systems and the application of fractional differentiation. As this volume covers recent applications of fractional calculus, it will be of interest to engineers, scientists, and applied mathematicians.
Author: Rainer Klages
Publisher: John Wiley & Sons
Release Date: 2008-09-02
This multi-author reference work provides a unique introduction to the currently emerging, highly interdisciplinary field of those transport processes that cannot be described by using standard methods of statistical mechanics. It comprehensively summarizes topics ranging from mathematical foundations of anomalous dynamics to the most recent experiments in this field. In so doing, this monograph extracts and emphasizes common principles and methods from many different disciplines while providing up-to-date coverage of this new field of research, considering such diverse applications as plasma physics, glassy material, cell science, and socio-economic aspects. The book will be of interest to both theorists and experimentalists in nonlinear dynamics, statistical physics and stochastic processes. It also forms an ideal starting point for graduate students moving into this area. 18 chapters written by internationally recognized experts in this field provide in-depth introductions to the following fundamental aspects of anomalous transport: * Fractional calculus and stochastic theory * Dynamical systems and deterministic transport * Anomalous transport in disordered systems * Applications to complex systems and experimental results.
In the 20 years since the pilot plant experiments used to develop the concept of electroviscoelasticity, inroads have been made in the understanding of its many related processes. Interfacial Electroviscoelasticity and Electrophoresis meets a massive scientific challenge by presenting deeper research and developments in the basic and applied science and engineering of finely dispersed particles and related systems. Introducing more profound and in-depth treatises related to the liquid-liquid finely dispersed systems (i.e., emulsions and double emulsions), this book describes a new theory developed through the authors’ work. These findings are likely to impact other research and applications in a wide array of other fields, considering that the modeling of liquid-liquid interfaces is key to numerous chemical manufacturing processes, including those used for emulsions, suspensions, nanopowders, foams, biocolloids, and plasmas. The authors cover phenomena at the micro, nano, and atto-scales, and their techniques, theory, and supporting data will be of particular interest to nanoscientists, especially with regard to the breaking of emulsions. This groundbreaking book: Takes an interdisciplinary approach to elucidate the momentum transfer and electron transfer phenomena Covers less classical chemical engineering insight and modern molecular and atomic engineering Reviews basic theory of electrokinetics, using the electrophoresis of rigid particles as an example Built around the central themes of hydrodynamic, electrodynamic, and thermodynamic instabilities that occur at interfaces, this book addresses recently developed concepts in the physics, chemistry, and rheological properties of those well-studied interfaces of rigid and deformable particles in homo- and hetero-aggregate dispersed systems. The book also introduces the key phenomenon of electrophoresis, since it is widely adopted either as an analytical tool to characterize the surface properties of colloid-sized particles or in the separation and purification process of both laboratory and industrial scales. The applications and implications of the material presented in the book represent a major contribution to the advanced fundamental, applied, and engineering research of interfacial and colloidal phenomena.