Fractional Order Crowd Dynamics
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Fractional Order Crowd Dynamics
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Author : Kecai Cao
language : en
Publisher: Walter de Gruyter GmbH & Co KG
Release Date : 2018-06-11
Fractional Order Crowd Dynamics written by Kecai Cao and has been published by Walter de Gruyter GmbH & Co KG this book supported file pdf, txt, epub, kindle and other format this book has been release on 2018-06-11 with Mathematics categories.
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.
Basic Theory
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Author : Anatoly Kochubei
language : en
Publisher: Walter de Gruyter GmbH & Co KG
Release Date : 2019-02-19
Basic Theory written by Anatoly Kochubei and has been published by Walter de Gruyter GmbH & Co KG this book supported file pdf, txt, epub, kindle and other format this book has been release on 2019-02-19 with Mathematics categories.
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.
Economic Dynamics With Memory
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Author : Vasily E. Tarasov
language : en
Publisher: Walter de Gruyter GmbH & Co KG
Release Date : 2021-01-18
Economic Dynamics With Memory written by Vasily E. Tarasov and has been published by Walter de Gruyter GmbH & Co KG this book supported file pdf, txt, epub, kindle and other format this book has been release on 2021-01-18 with Business & Economics categories.
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.
Fractional Differential Equations
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Author : Mouffak Benchohra
language : en
Publisher: Springer Nature
Release Date : 2023-07-10
Fractional Differential Equations written by Mouffak Benchohra and has been published by Springer Nature this book supported file pdf, txt, epub, kindle and other format this book has been release on 2023-07-10 with Mathematics categories.
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.
Crowd Dynamics By Kinetic Theory Modeling
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Author : Bouchra Aylaj
language : en
Publisher: Springer Nature
Release Date : 2022-06-01
Crowd Dynamics By Kinetic Theory Modeling written by Bouchra Aylaj and has been published by Springer Nature this book supported file pdf, txt, epub, kindle and other format this book has been release on 2022-06-01 with Mathematics categories.
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.
Fractional Signals And Systems
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Author : Manuel Duarte Ortigueira
language : en
Publisher: Walter de Gruyter GmbH & Co KG
Release Date : 2020-03-09
Fractional Signals And Systems written by Manuel Duarte Ortigueira and has been published by Walter de Gruyter GmbH & Co KG this book supported file pdf, txt, epub, kindle and other format this book has been release on 2020-03-09 with Mathematics categories.
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.
Fractional Hermite Hadamard Inequalities
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Author : JinRong Wang
language : en
Publisher: Walter de Gruyter GmbH & Co KG
Release Date : 2018-05-22
Fractional Hermite Hadamard Inequalities written by JinRong Wang and has been published by Walter de Gruyter GmbH & Co KG this book supported file pdf, txt, epub, kindle and other format this book has been release on 2018-05-22 with Mathematics categories.
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
Advanced Topics In Fractional Differential Equations
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Author : Mouffak Benchohra
language : en
Publisher: Springer Nature
Release Date : 2023-05-11
Advanced Topics In Fractional Differential Equations written by Mouffak Benchohra and has been published by Springer Nature this book supported file pdf, txt, epub, kindle and other format this book has been release on 2023-05-11 with Mathematics categories.
This book explores fractional differential equations with a fixed point approach. The authors highlight the existence, uniqueness, and stability results for various classes of fractional differential equations. All of the problems in the book also deal with some form of of the well-known Hilfer fractional derivative, which unifies the Riemann-Liouville and Caputo fractional derivatives. Classical and new fixed point theorems, associated with the measure of noncompactness in Banach spaces as well as several generalizations of the Gronwall's lemma, are employed as tools. The book is based on many years of research in this area, and provides suggestions for further study as well. The authors have included illustrations in order to support the readers’ understanding of the concepts presented. Includes illustrations in order to support readers understanding of the presented concepts · Approaches the topic of fractional differential equations while employing fixed point theorems as tools · Presents novel results, which build upon previous literature and many years of research by the authors
System And Data Driven Methods And Algorithms
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Author : Peter Benner
language : en
Publisher: Walter de Gruyter GmbH & Co KG
Release Date : 2021-11-08
System And Data Driven Methods And Algorithms written by Peter Benner and has been published by Walter de Gruyter GmbH & Co KG this book supported file pdf, txt, epub, kindle and other format this book has been release on 2021-11-08 with Mathematics categories.
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.
Modeling Of Discrete And Continuous Systems
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Author : Mohamed Kharrat
language : en
Publisher: Springer Nature
Release Date : 2025-02-27
Modeling Of Discrete And Continuous Systems written by Mohamed Kharrat and has been published by Springer Nature this book supported file pdf, txt, epub, kindle and other format this book has been release on 2025-02-27 with Mathematics categories.
This book contains a comprehensive collection of chapters on recent and original research, along with review articles, on mathematical modeling of dynamical systems described by various types of differential equations. Structured into 18 chapters dedicated to exploring different aspects of differential equations and their applications in modeling both discrete and continuous systems, it highlights theoretical advancements in mathematics and their practical applications in modeling dynamic systems. Readers will find contributions by renowned scholars who delve into the intricacies of nonlinear dynamics, stochastic processes, and partial differential equations. This book is an essential resource for researchers, academicians, and practitioners in the field of mathematical modeling.