Nature S Patterns And The Fractional Calculus
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Nature S Patterns And The Fractional Calculus
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Author : Bruce J. West
language : en
Publisher: Walter de Gruyter GmbH & Co KG
Release Date : 2017-09-11
Nature S Patterns And The Fractional Calculus written by Bruce J. West 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 2017-09-11 with Mathematics categories.
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
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Author : Bruce J. West
language : en
Publisher:
Release Date : 2017
Nature S Patterns And The Fractional Calculus written by Bruce J. West and has been published by this book supported file pdf, txt, epub, kindle and other format this book has been release on 2017 with Allometry categories.
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.
Complexus Mundi Emergent Patterns In Nature
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Author : Miroslav M Novak
language : en
Publisher: World Scientific
Release Date : 2006-01-26
Complexus Mundi Emergent Patterns In Nature written by Miroslav M Novak and has been published by World Scientific this book supported file pdf, txt, epub, kindle and other format this book has been release on 2006-01-26 with Science categories.
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.
Optimal Input Signals For Parameter Estimation
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Author : Ewaryst Rafajłowicz
language : en
Publisher: Walter de Gruyter GmbH & Co KG
Release Date : 2022-03-07
Optimal Input Signals For Parameter Estimation written by Ewaryst Rafajłowicz 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 2022-03-07 with History categories.
The aim of this book is to provide methods and algorithms for the optimization of input signals so as to estimate parameters in systems described by PDE’s as accurate as possible under given constraints. The optimality conditions have their background in the optimal experiment design theory for regression functions and in simple but useful results on the dependence of eigenvalues of partial differential operators on their parameters. Examples are provided that reveal sometimes intriguing geometry of spatiotemporal input signals and responses to them. An introduction to optimal experimental design for parameter estimation of regression functions is provided. The emphasis is on functions having a tensor product (Kronecker) structure that is compatible with eigenfunctions of many partial differential operators. New optimality conditions in the time domain and computational algorithms are derived for D-optimal input signals when parameters of ordinary differential equations are estimated. They are used as building blocks for constructing D-optimal spatio-temporal inputs for systems described by linear partial differential equations of the parabolic and hyperbolic types with constant parameters. Optimality conditions for spatially distributed signals are also obtained for equations of elliptic type in those cases where their eigenfunctions do not depend on unknown constant parameters. These conditions and the resulting algorithms are interesting in their own right and, moreover, they are second building blocks for optimality of spatio-temporal signals. A discussion of the generalizability and possible applications of the results obtained is presented.
Advanced Mathematical Methods
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Author : Francesco Mainardi
language : en
Publisher: MDPI
Release Date : 2020-02-05
Advanced Mathematical Methods written by Francesco Mainardi and has been published by MDPI this book supported file pdf, txt, epub, kindle and other format this book has been release on 2020-02-05 with Mathematics categories.
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
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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.
Fractional Differential Equations And Inclusions Classical And Advanced Topics
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Author : Said Abbas
language : en
Publisher: World Scientific
Release Date : 2023-02-02
Fractional Differential Equations And Inclusions Classical And Advanced Topics written by Said Abbas and has been published by World Scientific this book supported file pdf, txt, epub, kindle and other format this book has been release on 2023-02-02 with Mathematics categories.
This monograph is devoted to the existence and stability (Ulam-Hyers-Rassias stability and asymptotic stability) of solutions for various classes of functional differential equations or inclusions involving the Hadamard or Hilfer fractional derivative. Some equations present delay which may be finite, infinite, or state-dependent. Others are subject to impulsive effect which may be fixed or non-instantaneous.Readers will find the book self-contained and unified in presentation. It provides the necessary background material required to go further into the subject and explores the rich research literature in detail. Each chapter concludes with a section devoted to notes and bibliographical remarks and all abstract results are illustrated by examples. The tools used include many classical and modern nonlinear analysis methods such as fixed-point theorems, as well as some notions of Ulam stability, attractivity and the measure of non-compactness as well as the measure of weak noncompactness. It is useful for researchers and graduate students for research, seminars, and advanced graduate courses, in pure and applied mathematics, physics, mechanics, engineering, biology, and all other applied sciences.
Crucial Event Rehabilitation Therapy
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Author : Bruce J. West
language : en
Publisher: Springer Nature
Release Date : 2023-11-30
Crucial Event Rehabilitation Therapy written by Bruce J. West and has been published by Springer Nature this book supported file pdf, txt, epub, kindle and other format this book has been release on 2023-11-30 with Mathematics categories.
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 anideal 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.
Fractional Difference Differential Equations And Inclusions
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Author : Saïd Abbas
language : en
Publisher: Elsevier
Release Date : 2024-01-11
Fractional Difference Differential Equations And Inclusions written by Saïd Abbas and has been published by Elsevier this book supported file pdf, txt, epub, kindle and other format this book has been release on 2024-01-11 with Mathematics categories.
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
Hausdorff Calculus
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Author : Yingjie Liang
language : en
Publisher: Walter de Gruyter GmbH & Co KG
Release Date : 2019-03-04
Hausdorff Calculus written by Yingjie Liang 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 2019-03-04 with Mathematics categories.
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.