Fractional Order Crowd Dynamics
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| Author | : Kecai Cao |
| Publisher | : Walter de Gruyter GmbH & Co KG |
| Total Pages | : 138 |
| Release | : 2018-06-11 |
| Genre | : Mathematics |
| ISBN | : 311047283X |
Download Fractional Order Crowd Dynamics Book in PDF, Epub and Kindle
This book illustrates the application of fractional calculus in crowd dynamics via modeling and control groups of pedestrians. Decision-making processes, conservation laws of mass/momentum, and micro-macro models are employed to describe system dynamics while cooperative movements in micro scale, and fractional diffusion in macro scale are studied to control the group of pedestrians. Obtained work is included in the Intelligent Evacuation Systems that is used for modeling and to control crowds of pedestrians. With practical issues considered, this book is of interests to mathematicians, physicists, and engineers.
| Author | : Anatoly Kochubei |
| Publisher | : Walter de Gruyter GmbH & Co KG |
| Total Pages | : 489 |
| Release | : 2019-02-19 |
| Genre | : Mathematics |
| ISBN | : 3110571625 |
Download Basic Theory Book in PDF, Epub and Kindle
This multi-volume handbook is the most up-to-date and comprehensive reference work in the field of fractional calculus and its numerous applications. This first volume collects authoritative chapters covering the mathematical theory of fractional calculus, including fractional-order operators, integral transforms and equations, special functions, calculus of variations, and probabilistic and other aspects.
| Author | : Vasily E. Tarasov |
| Publisher | : Walter de Gruyter GmbH & Co KG |
| Total Pages | : 602 |
| Release | : 2021-01-18 |
| Genre | : Business & Economics |
| ISBN | : 3110627450 |
Download Economic Dynamics with Memory Book in PDF, Epub and Kindle
This book presents the applications of fractional calculus, fractional operators of non-integer orders and fractional differential equations in describing economic dynamics with long memory. Generalizations of basic economic concepts, notions and methods for the economic processes with memory are suggested. New micro and macroeconomic models with continuous time are proposed to describe the fractional economic dynamics with long memory as well.
| Author | : Mouffak Benchohra |
| Publisher | : Springer Nature |
| Total Pages | : 197 |
| Release | : 2023-07-10 |
| Genre | : Mathematics |
| ISBN | : 303134877X |
Download Fractional Differential Equations Book in PDF, Epub and Kindle
This book covers problems involving a variety of fractional differential equations, as well as some involving the generalized Hilfer fractional derivative, which unifies the Riemann-Liouville and Caputo fractional derivatives. The authors highlight the existence, uniqueness, and stability results for various classes of fractional differential equations based on the most recent research in the area. The book discusses the classic and novel fixed point theorems related to the measure of noncompactness in Banach spaces and explains how to utilize them as tools. The authors build each chapter upon the previous one, helping readers to develop their understanding of the topic. The book includes illustrated results, analysis, and suggestions for further study.
| Author | : Bouchra Aylaj |
| Publisher | : Springer Nature |
| Total Pages | : 86 |
| Release | : 2022-06-01 |
| Genre | : Mathematics |
| ISBN | : 3031024281 |
Download Crowd Dynamics by Kinetic Theory Modeling Book in PDF, Epub and Kindle
The contents of this brief Lecture Note are devoted to modeling, simulations, and applications with the aim of proposing a unified multiscale approach accounting for the physics and the psychology of people in crowds. The modeling approach is based on the mathematical theory of active particles, with the goal of contributing to safety problems of interest for the well-being of our society, for instance, by supporting crisis management in critical situations such as sudden evacuation dynamics induced through complex venues by incidents.
| Author | : Manuel Duarte Ortigueira |
| Publisher | : Walter de Gruyter GmbH & Co KG |
| Total Pages | : 298 |
| Release | : 2020-03-09 |
| Genre | : Mathematics |
| ISBN | : 3110624583 |
Download Fractional Signals and Systems Book in PDF, Epub and Kindle
The book illustrates the theoretical results of fractional derivatives via applications in signals and systems, covering continuous and discrete derivatives, and the corresponding linear systems. Both time and frequency analysis are presented. Some advanced topics are included like derivatives of stochastic processes. It is an essential reference for researchers in mathematics, physics, and engineering.
| Author | : JinRong Wang |
| Publisher | : Walter de Gruyter GmbH & Co KG |
| Total Pages | : 387 |
| Release | : 2018-05-22 |
| Genre | : Mathematics |
| ISBN | : 3110523620 |
Download Fractional Hermite-Hadamard Inequalities Book in PDF, Epub and Kindle
This book extends classical Hermite-Hadamard type inequalities to the fractional case via establishing fractional integral identities, and discusses Riemann-Liouville and Hadamard integrals, respectively, by various convex functions. Illustrating theoretical results via applications in special means of real numbers, it is an essential reference for applied mathematicians and engineers working with fractional calculus. Contents Introduction Preliminaries Fractional integral identities Hermite-Hadamard inequalities involving Riemann-Liouville fractional integrals Hermite-Hadamard inequalities involving Hadamard fractional integrals
| Author | : Yingjie Liang |
| Publisher | : Walter de Gruyter GmbH & Co KG |
| Total Pages | : 146 |
| Release | : 2019-03-04 |
| Genre | : Mathematics |
| ISBN | : 3110608529 |
Download Hausdorff Calculus Book in PDF, Epub and Kindle
This book introduces the fundamental concepts, methods, and applications of Hausdorff calculus, with a focus on its applications in fractal systems. Topics such as the Hausdorff diffusion equation, Hausdorff radial basis function, Hausdorff derivative nonlinear systems, PDE modeling, statistics on fractals, etc. are discussed in detail. It is an essential reference for researchers in mathematics, physics, geomechanics, and mechanics.
| Author | : Peter Benner |
| Publisher | : Walter de Gruyter GmbH & Co KG |
| Total Pages | : 388 |
| Release | : 2021-11-08 |
| Genre | : Mathematics |
| ISBN | : 3110498960 |
Download System- and Data-Driven Methods and Algorithms Book in PDF, Epub and Kindle
An increasing complexity of models used to predict real-world systems leads to the need for algorithms to replace complex models with far simpler ones, while preserving the accuracy of the predictions. This two-volume handbook covers methods as well as applications. This first volume focuses on real-time control theory, data assimilation, real-time visualization, high-dimensional state spaces and interaction of different reduction techniques.
| Author | : Livio Gibelli |
| Publisher | : |
| Total Pages | : 292 |
| Release | : 2018 |
| Genre | : Statistical physics |
| ISBN | : 9783030051303 |
Download Crowd Dynamics, Volume 1 Book in PDF, Epub and Kindle
This volume explores the complex problems that arise in the modeling and simulation of crowd dynamics in order to present the state-of-the-art of this emerging field and contribute to future research activities. Experts in various areas apply their unique perspectives to specific aspects of crowd dynamics, covering the topic from multiple angles. These include a demonstration of how virtual reality may solve dilemmas in collecting empirical data; a detailed study on pedestrian movement in smoke-filled environments; a presentation of one-dimensional conservation laws with point constraints on the flux; a collection of new ideas on the modeling of crowd dynamics at the microscopic scale; and others. Applied mathematicians interested in crowd dynamics, pedestrian movement, traffic flow modeling, urban planning, and other topics will find this volume a valuable resource. Additionally, researchers in social psychology, architecture, and engineering may find this information relevant to their work.
