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Natures Patterns And The Fractional Calculus
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Book Synopsis Nature’s Patterns and the Fractional Calculus by : Bruce J. West
Download or read book Nature’s Patterns and the Fractional Calculus written by Bruce J. West and published by Walter de Gruyter GmbH & Co KG. This book was released on 2017-09-11 with total page 244 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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
Book Synopsis Nature’s Patterns and the Fractional Calculus by : Bruce J. West
Download or read book Nature’s Patterns and the Fractional Calculus written by Bruce J. West and published by Walter de Gruyter GmbH & Co KG. This book was released on 2017-09-11 with total page 214 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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
Book Synopsis Advances in Fractional Calculus by : J. Sabatier
Download or read book Advances in Fractional Calculus written by J. Sabatier and published by Springer Science & Business Media. This book was released on 2007-07-28 with total page 550 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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.
Book Synopsis Emergent Nature: Patterns, Growth And Scaling In The Sciences by : Miroslav M Novak
Download or read book Emergent Nature: Patterns, Growth And Scaling In The Sciences written by Miroslav M Novak and published by World Scientific. This book was released on 2002-02-04 with total page 458 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book, based on presentations made at the international conference Fractals 2002, is of interest to everyone in the general field of nonlinear dynamics. The abundance of papers from numerous disciplines makes it exciting reading and provides a unifying thread through the topics, such as ray tracing, structure of peptides, modeling fractal surfaces, cancer growth, macaque monkey cortical neurons, occurrence of earthquakes, and patterns of the World Wide Web.
Book Synopsis Complexus Mundi: Emergent Patterns In Nature by : Miroslav M Novak
Download or read book Complexus Mundi: Emergent Patterns In Nature written by Miroslav M Novak and published by World Scientific. This book was released on 2006-01-26 with total page 359 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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.
Book Synopsis Fractional Calculus And Waves In Linear Viscoelasticity: An Introduction To Mathematical Models (Second Edition) by : Francesco Mainardi
Download or read book Fractional Calculus And Waves In Linear Viscoelasticity: An Introduction To Mathematical Models (Second Edition) written by Francesco Mainardi and published by World Scientific. This book was released on 2022-08-16 with total page 626 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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.
Book Synopsis Fractional Calculus for Skeptics I by : Bruce J. West
Download or read book Fractional Calculus for Skeptics I written by Bruce J. West and published by CRC Press. This book was released on 2024-05-16 with total page 147 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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.
Book Synopsis Nature's Patterns and the Fractional Calculus by : Bruce J. West
Download or read book Nature's Patterns and the Fractional Calculus written by Bruce J. West and published by . This book was released on 2017 with total page pages. Available in PDF, EPUB and Kindle. Book excerpt: 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.
Book Synopsis Advanced Mathematical Methods by : Francesco Mainardi
Download or read book Advanced Mathematical Methods written by Francesco Mainardi and published by MDPI. This book was released on 2020-02-05 with total page 198 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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.
Book Synopsis Thinking In Patterns: Fractals And Related Phenomena In Nature by : Miroslav M Novak
Download or read book Thinking In Patterns: Fractals And Related Phenomena In Nature written by Miroslav M Novak and published by World Scientific. This book was released on 2004-03-09 with total page 336 pages. Available in PDF, EPUB and Kindle. Book excerpt: Fractal geometry, together with the broader fields of nonlinear dynamics and complexity, represented a large segment of modern science at the end of the 20th century. Penetration of the resulting new paradigms into practically all academic disciplines has confirmed the fundamental assertion of universal formalism common to a wide range of human endeavors.This book contains an extended article by B B Mandelbrot, reviewing his contribution to fractal geometry and outlining some unsolved problems, with illustrations especially of finance and physics. It covers a range of multidisciplinary topics — from the biology of aging, through the self-similar shape of plants, image decompression and solar magnetic fields, to sound reflection in the street. The book is a treasure trove for innovative researchers working in fields related to fractal geometry.The proceedings have been selected for coverage in:• Index to Scientific & Technical Proceedings® (ISTP® / ISI Proceedings)• Index to Scientific & Technical Proceedings (ISTP CDROM version / ISI Proceedings)• CC Proceedings — Engineering & Physical Sciences
Download or read book Basic Theory written by Anatoly Kochubei and published by Walter de Gruyter GmbH & Co KG. This book was released on 2019-02-19 with total page 490 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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.
Book Synopsis Hausdorff Calculus by : Yingjie Liang
Download or read book Hausdorff Calculus written by Yingjie Liang and published by Walter de Gruyter GmbH & Co KG. This book was released on 2019-03-04 with total page 148 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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.
Book Synopsis Crucial Event Rehabilitation Therapy by : Bruce J. West
Download or read book Crucial Event Rehabilitation Therapy written by Bruce J. West and published by Springer Nature. This book was released on 2023-11-30 with total page 101 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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.
Book Synopsis Fractional Difference, Differential Equations, and Inclusions by : Saïd Abbas
Download or read book Fractional Difference, Differential Equations, and Inclusions written by Saïd Abbas and published by Elsevier. This book was released on 2024-01-16 with total page 400 pages. Available in PDF, EPUB and Kindle. Book excerpt: The field of fractional calculus (FC) is more than 300 years old, and it presumably stemmed from a question about a fractional-order derivative raised in communication between L'Hopital and Leibniz in the year 1695. This branch of mathematical analysis is regarded as the generalization of classical calculus, as it deals with the derivative and integral operators of fractional order. The tools of fractional calculus are found to be of great utility in improving the mathematical modeling of many natural phenomena and processes occurring in the areas of engineering, social, natural, and biomedical sciences. Fractional Difference, Differential Equations, and Inclusions: Analysis and Stability is devoted to the existence and stability (Ulam-Hyers-Rassias stability and asymptotic stability) of solutions for several classes of functional fractional difference equations and inclusions. Some equations include delay effects of finite, infinite, or state-dependent nature. Others are subject to impulsive effect which may be fixed or non-instantaneous. The tools used to establish the existence results for the proposed problems include fixed point theorems, densifiability techniques, monotone iterative technique, notions of Ulam stability, attractivity and the measure of non-compactness as well as the measure of weak noncompactness. All the abstract results are illustrated by examples in applied mathematics, engineering, biomedical, and other applied sciences. Introduces notation, definitions, and foundational concepts of fractional q-calculus Presents existence and attractivity results for a class of implicit fractional q-difference equations in Banach and Fréchet spaces Focuses on the study of a class of coupled systems of Hilfer and Hilfer-Hadamard fractional differential equations
Book Synopsis Fractional Signals and Systems by : Manuel Duarte Ortigueira
Download or read book Fractional Signals and Systems written by Manuel Duarte Ortigueira and published by Walter de Gruyter GmbH & Co KG. This book was released on 2020-03-09 with total page 300 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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.
Book Synopsis Fractional-Order Equations and Inclusions by : Michal Fečkan
Download or read book Fractional-Order Equations and Inclusions written by Michal Fečkan and published by Walter de Gruyter GmbH & Co KG. This book was released on 2017-11-07 with total page 506 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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
Book Synopsis Fractional Hermite-Hadamard Inequalities by : JinRong Wang
Download or read book Fractional Hermite-Hadamard Inequalities written by JinRong Wang and published by Walter de Gruyter GmbH & Co KG. This book was released on 2018-05-22 with total page 390 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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
