Nature S Patterns And The Fractional Calculus

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Nature’s Patterns and the Fractional Calculus

Bruce J. West
Nature s Patterns and the Fractional Calculus Book PDF

Author : Bruce J. West
Publisher : Walter de Gruyter GmbH & Co KG
Page : 213 pages
File Size : 48,8 Mb
Release : 2017-09-11
Category : Mathematics
ISBN : 9783110534276

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Nature’s Patterns and the Fractional Calculus by Bruce J. West Pdf

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

Nature's Patterns and the Fractional Calculus

Bruce J. West
Nature s Patterns and the Fractional Calculus Book PDF

Author : Bruce J. West
Publisher : Unknown
Page : 128 pages
File Size : 46,8 Mb
Release : 2017
Category : Allometry
ISBN : 3110535149

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Nature's Patterns and the Fractional Calculus by Bruce J. West Pdf

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. ContentsComplexityEmpirical allometryStatistics, scaling and simulationAllometry theoriesStrange kineticsFractional probability calculus.

Nature’s Patterns and the Fractional Calculus

Bruce J. West
Nature s Patterns and the Fractional Calculus Book PDF

Author : Bruce J. West
Publisher : Walter de Gruyter GmbH & Co KG
Page : 213 pages
File Size : 48,8 Mb
Release : 2017-09-11
Category : Mathematics
ISBN : 9783110535136

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Nature’s Patterns and the Fractional Calculus by Bruce J. West Pdf

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

Complexus Mundi: Emergent Patterns In Nature

Miroslav M Novak
Complexus Mundi Emergent Patterns In Nature Book PDF

Author : Miroslav M Novak
Publisher : World Scientific
Page : 359 pages
File Size : 51,8 Mb
Release : 2006-01-26
Category : Science
ISBN : 9789814478557

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Complexus Mundi: Emergent Patterns In Nature by Miroslav M Novak Pdf

The dynamics of complex systems can clarify the creation of structures in Nature. This creation is driven by the collective interaction of constitutive elements of the system. Such interactions are frequently nonlinear and are directly responsible for the lack of prediction in the evolution process. The self-organization accompanying these processes occurs all around us and is constantly being rediscovered, under the guise of a new jargon, in apparently unrelated disciplines.This volume offers unique perspectives on aspects of fractals and complexity and, through the examination of complementary techniques, provides a unifying thread in this multidisciplinary endeavor. Do nonlinear interactions play a role in the complexity management of socio-econo-political systems? Is it possible to extract the global properties of genetic regulatory networks without knowing the details of individual genes? What can one learn by transplanting the self-organization effects known in laser processes to the study of emotions? What can the change in the level of complexity tell us about the physiological state of the organism? The reader will enjoy finding the answers to these questions and many more in this book.

Fractional Calculus View of Complexity

Bruce J. West
Fractional Calculus View of Complexity Book PDF

Author : Bruce J. West
Publisher : CRC Press
Page : 303 pages
File Size : 49,9 Mb
Release : 2016-01-05
Category : Mathematics
ISBN : 9781498738019

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Fractional Calculus View of Complexity by Bruce J. West Pdf

This book is not a text devoted to a pedagogical presentation of a specialized topic nor is it a monograph focused on the author's area of research. It accomplishes both these things while providing a rationale for why the reader ought to be interested in learning about fractional calculus. This book is for researchers who has heard about many

Fractional Calculus for Skeptics I

Bruce J. West,YangQuan Chen
Fractional Calculus for Skeptics I Book PDF

Author : Bruce J. West,YangQuan Chen
Publisher : CRC Press
Page : 147 pages
File Size : 48,7 Mb
Release : 2024-05-16
Category : Mathematics
ISBN : 9781040012697

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Fractional Calculus for Skeptics I by Bruce J. West,YangQuan Chen Pdf

This book is the first of its kind on fractional calculus (FC), dedicated to advocating for FC in STEM education and research. Fractional calculus is increasingly used today, but there remains a core population of skeptics regarding the utility of this "new" calculus. This book is intended for those who are skeptical about the need for fractional calculus to describe dynamic complex networks and must be convinced of its use on a case-by-case basis. It is a one-stop resource to rapidly read and replace the appropriate skepticism with new knowledge. It offers compelling reasons from the perspectives of the physical, social, and life sciences as to why fractional calculus is needed when addressing the complexity of an underlying STEM phenomenon. The six chapters are accompanied by useful and essential appendices and chapter-end references. Each includes new (fractional-order) ways of thinking about statistics, complexity dynamics, and what constitutes a solution to a complexity science problem. The book will appeal to students and researchers in all STEM-related fields, such as engineering, physics, biology and biomedicine, climate change, big data, and machine learning. It is also suitable for general readers interested in these fields.

General Fractional Derivatives

Xiao-Jun Yang
General Fractional Derivatives Book PDF

Author : Xiao-Jun Yang
Publisher : CRC Press
Page : 306 pages
File Size : 48,7 Mb
Release : 2019-05-10
Category : Mathematics
ISBN : 9780429811524

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General Fractional Derivatives by Xiao-Jun Yang Pdf

General Fractional Derivatives: Theory, Methods and Applications provides knowledge of the special functions with respect to another function, and the integro-differential operators where the integrals are of the convolution type and exist the singular, weakly singular and nonsingular kernels, which exhibit the fractional derivatives, fractional integrals, general fractional derivatives, and general fractional integrals of the constant and variable order without and with respect to another function due to the appearance of the power-law and complex herbivores to figure out the modern developments in theoretical and applied science. Features: Give some new results for fractional calculus of constant and variable orders. Discuss some new definitions for fractional calculus with respect to another function. Provide definitions for general fractional calculus of constant and variable orders. Report new results of general fractional calculus with respect to another function. Propose news special functions with respect to another function and their applications. Present new models for the anomalous relaxation and rheological behaviors. This book serves as a reference book and textbook for scientists and engineers in the fields of mathematics, physics, chemistry and engineering, senior undergraduate and graduate students. Dr. Xiao-Jun Yang is a full professor of Applied Mathematics and Mechanics, at China University of Mining and Technology, China. He is currently an editor of several scientific journals, such as Fractals, Applied Numerical Mathematics, Mathematical Modelling and Analysis, International Journal of Numerical Methods for Heat & Fluid Flow, and Thermal Science.

Fractional Calculus And Waves In Linear Viscoelasticity: An Introduction To Mathematical Models (Second Edition)

Francesco Mainardi
Fractional Calculus And Waves In Linear Viscoelasticity An Introduction To Mathematical Models Second Edition Book PDF

Author : Francesco Mainardi
Publisher : World Scientific
Page : 626 pages
File Size : 43,8 Mb
Release : 2022-08-16
Category : Mathematics
ISBN : 9781783264001

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Fractional Calculus And Waves In Linear Viscoelasticity: An Introduction To Mathematical Models (Second Edition) by Francesco Mainardi Pdf

Fractional Calculus and Waves in Linear Viscoelasticity (Second Edition) is a self-contained treatment of the mathematical theory of linear (uni-axial) viscoelasticity (constitutive equation and waves) with particular regard to models based on fractional calculus. It serves as a general introduction to the above-mentioned areas of mathematical modeling. The explanations in the book are detailed enough to capture the interest of the curious reader, and complete enough to provide the necessary background material needed to delve further into the subject and explore the research literature. In particular the relevant role played by some special functions is pointed out along with their visualization through plots. Graphics are extensively used in the book and a large general bibliography is included at the end.This new edition keeps the structure of the first edition but each chapter has been revised and expanded, and new additions include a novel appendix on complete monotonic and Bernstein functions that are known to play a fundamental role in linear viscoelasticity.This book is suitable for engineers, graduate students and researchers interested in fractional calculus and continuum mechanics.

Advanced Mathematical Methods

Francesco Mainardi,Andrea Giusti
Advanced Mathematical Methods Book PDF

Author : Francesco Mainardi,Andrea Giusti
Publisher : MDPI
Page : 198 pages
File Size : 50,8 Mb
Release : 2020-02-05
Category : Mathematics
ISBN : 9783039282463

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Advanced Mathematical Methods by Francesco Mainardi,Andrea Giusti Pdf

The many technical and computational problems that appear to be constantly emerging in various branches of physics and engineering beg for a more detailed understanding of the fundamental mathematics that serves as the cornerstone of our way of understanding natural phenomena. The purpose of this Special Issue was to establish a brief collection of carefully selected articles authored by promising young scientists and the world's leading experts in pure and applied mathematics, highlighting the state-of-the-art of the various research lines focusing on the study of analytical and numerical mathematical methods for pure and applied sciences.

Basic Theory

Anatoly Kochubei,Yuri Luchko
Basic Theory Book PDF

Author : Anatoly Kochubei,Yuri Luchko
Publisher : Walter de Gruyter GmbH & Co KG
Page : 489 pages
File Size : 43,8 Mb
Release : 2019-02-19
Category : Mathematics
ISBN : 9783110571622

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Basic Theory by Anatoly Kochubei,Yuri Luchko Pdf

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.

Crucial Event Rehabilitation Therapy

Bruce J. West,Paolo Grigolini,Mauro Bologna
Crucial Event Rehabilitation Therapy Book PDF

Author : Bruce J. West,Paolo Grigolini,Mauro Bologna
Publisher : Springer Nature
Page : 101 pages
File Size : 46,9 Mb
Release : 2023-11-30
Category : Mathematics
ISBN : 9783031462771

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Crucial Event Rehabilitation Therapy by Bruce J. West,Paolo Grigolini,Mauro Bologna Pdf

This book describes a new strategy for rehabilitation from injury and/or disease using Crucial Event Therapy. Recent studies have shown that individuals can recuperate more rapidly from surgery and other invasive procedures intended to correct the negative effects of disease or injury through the use of life support systems that operate at the body's natural biofrequencies. The same observation has been clinically shown to reverse the degenerative effects of neurodegenerative diseases such as Parkinson’s and Alzheimer's Disease. Crucial Event Therapy describes medicine as the operational control of the functions of the human body treated as a network-of-networks, with 1/f-variable crucial events coding the dynamic states of health and disease through information flow within a network and information exchange between biomedical networks. A new way of thinking based on the statistics of Cortical Events is presented and the relevant literature is suitably referenced. This is an ideal book for biophysicists and data scientists seeking to understand the connection of complexity measures for the study of consciousness with the clinical aspects of designing a rehabilitation strategy.

Hausdorff Calculus

Yingjie Liang,Wen Chen,Wei Cai
Hausdorff Calculus Book PDF

Author : Yingjie Liang,Wen Chen,Wei Cai
Publisher : Walter de Gruyter GmbH & Co KG
Page : 146 pages
File Size : 50,5 Mb
Release : 2019-03-04
Category : Mathematics
ISBN : 9783110608526

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Hausdorff Calculus by Yingjie Liang,Wen Chen,Wei Cai Pdf

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.

Nonlinear Dynamics and Pattern Formation in the Natural Environment

A. Van Harten,A. Doelman
Nonlinear Dynamics and Pattern Formation in the Natural Environment Book PDF

Author : A. Van Harten,A. Doelman
Publisher : Taylor & Francis
Page : 350 pages
File Size : 41,5 Mb
Release : 2022-09-16
Category : Mathematics
ISBN : 9781351428262

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Nonlinear Dynamics and Pattern Formation in the Natural Environment by A. Van Harten,A. Doelman Pdf

This Research Note aims to provide an insight into recent developments in the theory of pattern formation. In the last decade there has been considerable progress in this field, both from a theoretical and a practical point of view. Recent mathematical developments concern the study of the nonlinear stability of systems at near-critical conditions by an appropriate system of modulation equations. The complexity of the original problem can be reduced drastically by this approximation. Moreover, it provides unifying point of view for a wide range of problems. New applications of the theory arise in a multitude of scientific areas such as hydrodynamics, reaction-diffusion problems, oceanography, meteorology, combustion, geophysical and biological morphodynamics and semi-conductors.This book is intended to show the interactions between the mathematical theory of nonlinear dynamics and the study of pattern generating phenomena in the natural environment. There is an intimate relationship between new insights in the mathematical aspects of nonlinear pattern formation and the comprehension of such phenomena. Therefore there are two partly overlapping main themes: one in which the emphasis is on generally applicable mathematical theories and techniques and one in which the phenomenology of pattern evolution in various areas is discussed.The book comprises 19 contributions by experts in the field. Although the emphasis changes considerably from paper to paper, in each contribution the same two themes are present; all the authors have aimed to achieve a suitable balance between the mathematical theory and the physical phenomena.

Fractional Signals and Systems

Manuel Duarte Ortigueira,Duarte Valério
Fractional Signals and Systems Book PDF

Author : Manuel Duarte Ortigueira,Duarte Valério
Publisher : Walter de Gruyter GmbH & Co KG
Page : 298 pages
File Size : 44,6 Mb
Release : 2020-03-09
Category : Mathematics
ISBN : 9783110624588

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Fractional Signals and Systems by Manuel Duarte Ortigueira,Duarte Valério Pdf

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

JinRong Wang,Michal Fečkan
Fractional Hermite Hadamard Inequalities Book PDF

Author : JinRong Wang,Michal Fečkan
Publisher : Walter de Gruyter GmbH & Co KG
Page : 387 pages
File Size : 49,9 Mb
Release : 2018-05-22
Category : Mathematics
ISBN : 9783110522440

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Fractional Hermite-Hadamard Inequalities by JinRong Wang,Michal Fečkan Pdf

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