Veröffentlicht von De Gruyter

Fractional Calculus in Applied Sciences and Engineering

Herausgegeben von: Changpin Li

ISSN: 2509-7210

e-ISSN 2509-7229

Übersicht
Bände

The series is devoted to the publication of high-level monographs which cover progresses in fractional calculus research in mathematics and applications in physics, mechanics, engineering and biology etc. Methodological aspects e.g., theory, modeling and computational methods are presented from mathematical point of view, and emphases are placed in computer simulation, analysis, design and control of application-oriented issues in various scientific disciplines. It is designed for mathematicians, and researchers using fractional calculus as a tool in the field of physics, mechanics, engineering and biology. Contributions which are interdisciplinary and which stimulate further research at the crossroads of sciences and engineering are particularly welcomed.

Editor-in-chief: Changpin Li, Shanghai University, China

Editorial Board:
Virginia Kiryakova, Bulgarian Academy of Sciences, Bulgaria
Francesco Mainardi, University of Bologna, Italy
Dragan Spasic, University of Novi Sad, Serbia
Bruce Ian Henry, University of New South Wales, Australia
YangQuan Chen, University of California, Merced, USA

Please submit book proposals to Leonardo Milla, leonardo.milla@degruyter.com

Fachgebiete

Buch 2024

Fractional Differential Equations

A Coincidence Degree Approach

Mouffak Benchohra, Soufyane Bouriah, Abdelkrim Salim, Yong Zhou

Band 12 in dieser Reihe

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This book is devoted to the existence and uniqueness results for various classes of problems with periodic conditions. All of the problems in this book deal with fractional differential equations and some fractional derivatives such as the Riemann-Liouville, Caputo and Hilfer fractional derivatives. Classical fixed point theorems as well as the coincidence degree theory of Mawhin are employed as tools.

DOI:: https://doi.org/10.1515/9783111334387
ISBN:: 9783111334387
ISBN:: 9783111334462
ISBN:: 9783111334349
Fachgebiet:: Technik
Fachgebiet:: Einführungen und Gesamtdarstellungen
Fachgebiet:: Technische Grundlagen und Werkzeuge
Fachgebiet:: Mathematik
Fachgebiet:: Differentialgleichungen und dynamische Systeme
Fachgebiet:: Angewandte Mathematik
Verlag:: De Gruyter

Buch 2022

Theory of Fractional Evolution Equations

Yong Zhou, Bashir Ahmad, Ahmed Alsaedi

Band 11 in dieser Reihe

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Fractional evolution equations provide a unifying framework to investigate wellposedness of complex systems with fractional order derivatives. This monograph presents the existence, attractivity, stability, periodic solutions and control theory for time fractional evolution equations. The book contains an up-to-date and comprehensive stuff on the topic.

DOI:: https://doi.org/10.1515/9783110769272
ISBN:: 9783110769272
ISBN:: 9783110769364
ISBN:: 9783110769180
Fachgebiet:: Technik
Fachgebiet:: Einführungen und Gesamtdarstellungen
Fachgebiet:: Technische Grundlagen und Werkzeuge
Fachgebiet:: Mathematik
Fachgebiet:: Angewandte Mathematik
Verlag:: De Gruyter

Buch 2022

Outliers in Control Engineering

Fractional Calculus Perspective

Paweł D. Domański, YangQuan Chen, Maciej Ławryńczuk

Band 10 in dieser Reihe

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Outliers play an important, though underestimated, role in control engineering. Traditionally they are unseen and neglected. In opposition, industrial practice gives frequent examples of their existence and their mostly negative impacts on the control quality. The origin of outliers is never fully known. Some of them are generated externally to the process (exogenous), like for instance erroneous observations, data corrupted by control systems or the effect of human intervention. Such outliers appear occasionally with some unknow probability shifting real value often to some strange and nonsense value. They are frequently called deviants, anomalies or contaminants. In most cases we are interested in their detection and removal.

However, there exists the second kind of outliers. Quite often strange looking data observations are not artificial data occurrences. They may be just representatives of the underlying generation mechanism being inseparable internal part of the process (endogenous outliers). In such a case they are not wrong and should be treated with cautiousness, as they may include important information about the dynamic nature of the process. As such they cannot be neglected nor simply removed. The Outlier should be detected, labelled and suitably treated. These activities cannot be performed without proper analytical tools and modeling approaches. There are dozens of methods proposed by scientists, starting from Gaussian-based statistical scoring up to data mining artificial intelligence tools. The research presented in this book presents novel approach incorporating non-Gaussian statistical tools and fractional calculus approach revealing new data analytics applied to this important and challenging task.

The proposed book includes a collection of contributions addressing different yet cohesive subjects, like dynamic modelling, classical control, advanced control, fractional calculus, statistical analytics focused on an ultimate goal: robust and outlier-proof analysis. All studied problems show that outliers play an important role and classical methods, in which outlier are not taken into account, do not give good results. Applications from different engineering areas are considered such as semiconductor process control and monitoring, MIMO peltier temperature control and health monitoring, networked control systems, and etc.

DOI:: https://doi.org/10.1515/9783110729122
ISBN:: 9783110729122
ISBN:: 9783110729139
ISBN:: 9783110729078
Fachgebiet:: Technik
Fachgebiet:: Elektrotechnik
Fachgebiet:: Mess-, Steuer- und Regelungstechnik
Fachgebiet:: Maschinenbau
Fachgebiet:: Werkzeuge und Methoden
Fachgebiet:: Mathematik
Fachgebiet:: Angewandte Mathematik
Verlag:: De Gruyter

Buch 2021

Theory of Fractional Engineering Vibrations

Ming Li

Band 9 in dieser Reihe

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Vibration is important subject in many fields, ranging from mechanical engineering to electronic one. This book aims at giving a combination of conventional linear vibrations with recent fractional ones from a view of engineering. It consists of two parts. One is for conventional linear vibrations in Chapters 1 - 6 based on the authors lectures on the course of ship hull vibrations for undergraduates and postgraduates in Ocean College, Zhejiang University, China. The other, Chapters 7 - 15, contains his research in fractional vibrations.

the book is suitable for researchers and graduate students in science and engieering. Preferred preliminaries are calculus, university physics, theoretic mechanics, and material mechanics for readers.

DOI:: https://doi.org/10.1515/9783110726152
ISBN:: 9783110726152
ISBN:: 9783110726527
ISBN:: 9783110726169
Fachgebiet:: Technik
Fachgebiet:: Elektrotechnik
Fachgebiet:: Grundlagen der Elektrotechnik
Fachgebiet:: Maschinenbau
Fachgebiet:: Mechanik
Fachgebiet:: Mathematik
Fachgebiet:: Analysis
Fachgebiet:: Physik
Fachgebiet:: Mechanik und Fluiddynamik
Verlag:: De Gruyter

Buch 2021

Economic Dynamics with Memory

Fractional Calculus Approach

Vasily E. Tarasov, Valentina V. Tarasova

Band 8 in dieser Reihe

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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.

DOI:: https://doi.org/10.1515/9783110627459
ISBN:: 9783110627459
ISBN:: 9783110624601
ISBN:: 9783110624816
Fachgebiet:: Wirtschaftswissenschaften
Fachgebiet:: Mathematik und Statistik für Ökonomen
Fachgebiet:: Mathematik
Fachgebiet:: Technik
Fachgebiet:: Einführungen und Gesamtdarstellungen
Fachgebiet:: Technische Grundlagen und Werkzeuge
Fachgebiet:: Mathematik
Fachgebiet:: Analysis
Fachgebiet:: Differentialgleichungen und dynamische Systeme
Verlag:: De Gruyter

Buch 2020

Fractional Signals and Systems

Manuel Duarte Ortigueira, Duarte Valério

Band 7 in dieser Reihe

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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.

DOI:: https://doi.org/10.1515/9783110624588
ISBN:: 9783110624588
ISBN:: 9783110777161
ISBN:: 9783110621327
ISBN:: 9783110621297
Fachgebiet:: Technik
Fachgebiet:: Elektrotechnik
Fachgebiet:: Signalverarbeitung
Fachgebiet:: Mathematik
Fachgebiet:: Angewandte Mathematik
Verlag:: De Gruyter

Buch 2019

Hausdorff Calculus

Applications to Fractal Systems

Yingjie Liang, Wen Chen, Wei Cai

Band 6 in dieser Reihe

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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.

DOI:: https://doi.org/10.1515/9783110608526
ISBN:: 9783110608526
ISBN:: 9783110607055
ISBN:: 9783110606928
Fachgebiet:: Mathematik
Fachgebiet:: Differentialgleichungen und dynamische Systeme
Fachgebiet:: Angewandte Mathematik
Verlag:: De Gruyter

Buch 2018

Fractional Hermite-Hadamard Inequalities

JinRong Wang, Michal Fečkan

Band 5 in dieser Reihe

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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

DOI:: https://doi.org/10.1515/9783110523621
ISBN:: 9783110523621
ISBN:: 9783110522440
ISBN:: 9783110522204
Fachgebiet:: Mathematik
Fachgebiet:: Differentialgleichungen und dynamische Systeme
Fachgebiet:: Angewandte Mathematik
Verlag:: De Gruyter

Buch 2018

Fractional Order Crowd Dynamics

Cyber-Human System Modeling and Control

Kecai Cao, YangQuan Chen

Band 4 in dieser Reihe

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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.

DOI:: https://doi.org/10.1515/9783110473988
ISBN:: 9783110473988
ISBN:: 9783110472837
ISBN:: 9783110472813
Fachgebiet:: Mathematik
Fachgebiet:: Analysis
Fachgebiet:: Angewandte Mathematik
Verlag:: De Gruyter

Buch 2017

Fractional-Order Equations and Inclusions

Michal Fečkan, JinRong Wang, Michal Pospíšil

Band 3 in dieser Reihe

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This book presents fractional difference, integral, differential, evolution equations and inclusions, and discusses existence and asymptotic behavior of their solutions. Controllability and relaxed control results are obtained. Combining rigorous deduction with abundant examples, it is of interest to nonlinear science researchers using fractional equations as a tool, and physicists, mechanics researchers and engineers studying relevant topics.

Contents
Fractional Difference Equations
Fractional Integral Equations
Fractional Differential Equations
Fractional Evolution Equations: Continued
Fractional Differential Inclusions

DOI:: https://doi.org/10.1515/9783110522075
ISBN:: 9783110522075
ISBN:: 9783110521382
ISBN:: 9783110521559
Fachgebiet:: Mathematik
Fachgebiet:: Differentialgleichungen und dynamische Systeme
Fachgebiet:: Angewandte Mathematik
Verlag:: De Gruyter

Buch 2017

Nature’s Patterns and the Fractional Calculus

Bruce J. West

Band 2 in dieser Reihe

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Complexity increases with increasing system size in everything from organisms to organizations. The nonlinear dependence of a system’s functionality on its size, by means of an allometry relation, is argued to be a consequence of their joint dependency on complexity (information). In turn, complexity is proven to be the source of allometry and to provide a new kind of force entailed by a system‘s information gradient. Based on first principles, the scaling behavior of the probability density function is determined by the exact solution to a set of fractional differential equations. The resulting lowest order moments in system size and functionality gives rise to the empirical allometry relations. Taking examples from various topics in nature, the book is of interest to researchers in applied mathematics, as well as, investigators in the natural, social, physical and life sciences.

Contents
Complexity
Empirical allometry
Statistics, scaling and simulation
Allometry theories
Strange kinetics
Fractional probability calculus

DOI:: https://doi.org/10.1515/9783110535136
ISBN:: 9783110535136
ISBN:: 9783110534276
ISBN:: 9783110534115
Fachgebiet:: Mathematik
Fachgebiet:: Angewandte Mathematik
Fachgebiet:: Physik
Fachgebiet:: Nichtlineare und komplexe Systeme
Verlag:: De Gruyter

Buch 2017

Fractional-Order Control Systems

Fundamentals and Numerical Implementations

Dingyü Xue

Band 1 in dieser Reihe

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This book explains the essentials of fractional calculus and demonstrates its application in control system modeling, analysis and design. It presents original research to find high-precision solutions to fractional-order differentiations and differential equations. Numerical algorithms and their implementations are proposed to analyze multivariable fractional-order control systems. Through high-quality MATLAB programs, it provides engineers and applied mathematicians with theoretical and numerical tools to design control systems.

Contents
Introduction to fractional calculus and fractional-order control
Mathematical prerequisites
Definitions and computation algorithms of fractional-order derivatives and Integrals
Solutions of linear fractional-order differential equations
Approximation of fractional-order operators
Modelling and analysis of multivariable fractional-order transfer function Matrices
State space modelling and analysis of linear fractional-order Systems
Numerical solutions of nonlinear fractional-order differential Equations
Design of fractional-order PID controllers
Frequency domain controller design for multivariable fractional-order Systems
Inverse Laplace transforms involving fractional and irrational Operations
FOTF Toolbox functions and models
Benchmark problems for the assessment of fractional-order differential equation algorithms

DOI:: https://doi.org/10.1515/9783110497977
ISBN:: 9783110497977
ISBN:: 9783110499995
ISBN:: 9783110497199
Fachgebiet:: Technik
Fachgebiet:: Elektrotechnik
Fachgebiet:: Mess-, Steuer- und Regelungstechnik
Fachgebiet:: Mathematik
Fachgebiet:: Angewandte Mathematik
Verlag:: De Gruyter