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تعداد نتایج: 592

Physics of Fractal Operators

$This text describes the statistcal behavior of complex systems and shows how the fractional calculus can be used to model the behavior. The discussion emphasizes physical phenomena whose evolution is best described using the fractional calculus, such as systems with long-range spatial interactions or long-time memory. The book gives general strategies for understanding wave propagation through random media, the nonlinear response of complex materials, and the fluctuations of heat transport in heterogeneous materials.$

جزئیات و درخواست

By Bruce West, Mauro Bologna, Paolo Grigolini
Publisher: Springer Science & Business Media, 2012-12-06
Pages: 355
Language: en
ISBN_13:9780387217468
ISBN_10:0387217460
Subject: Science

Boundary Value Problems For Fractional Differential Equations And Systems

$This book is devoted to the study of existence of solutions or positive solutions for various classes of Riemann-Liouville and Caputo fractional differential equations, and systems of fractional differential equations subject to nonlocal boundary conditions. The monograph draws together many of the authors' results, that have been obtained and highly cited in the literature in the last four years.In each chapter, various examples are presented which support the main results. The methods used in the proof of these theorems include results from the fixed point theory and fixed point index theory. This volume can serve as a good resource for mathematical and scientific researchers, and for graduate students in mathematics and science interested in the existence of solutions for fractional differential equations and systems.$

جزئیات و درخواست

By Bashir Ahmad, Johnny L Henderson, Rodica Luca
Publisher: World Scientific, 2021-02-18
Pages: 468
Language: en
ISBN_13:9789811224478
ISBN_10:9811224471
Subject: Mathematics

General Fractional Derivatives with Applications in Viscoelasticity

$General Fractional Derivatives with Applications in Viscoelasticity introduces the newly established fractional-order calculus operators involving singular and non-singular kernels with applications to fractional-order viscoelastic models from the calculus operator viewpoint. Fractional calculus and its applications have gained considerable popularity and importance because of their applicability to many seemingly diverse and widespread fields in science and engineering. Many operations in physics and engineering can be defined accurately by using fractional derivatives to model complex phenomena. Viscoelasticity is chief among them, as the general fractional calculus approach to viscoelasticity has evolved as an empirical method of describing the properties of viscoelastic materials. General Fractional Derivatives with Applications in Viscoelasticity makes a concise presentation of general fractional calculus. - Presents a comprehensive overview of the fractional derivatives and their applications in viscoelasticity - Provides help in handling the power-law functions - Introduces and explores the questions about general fractional derivatives and its applications$

جزئیات و درخواست

By Xiao-Jun Yang, Feng Gao, Yang Ju
Publisher: Academic Press, 2020-04-03
Pages: 456
Language: en
ISBN_13:9780128172094
ISBN_10:0128172096
Subject: Mathematics

Numerical Methods for Fractional Calculus

$Numerical Methods for Fractional Calculus presents numerical methods for fractional integrals and fractional derivatives, finite difference methods for fractional ordinary differential equations (FODEs) and fractional partial differential equations (FPDEs), and finite element methods for FPDEs.The book introduces the basic definitions and propertie$

جزئیات و درخواست

By Changpin Li, Fanhai Zeng
Publisher: CRC Press, 2015-05-19
Pages: 299
Language: en
ISBN_13:9781482253818
ISBN_10:148225381X
Subject: Mathematics

Fractional Order Signal Processing

Introductory Concepts and Applications

$The book tries to briefly introduce the diverse literatures in the field of fractional order signal processing which is becoming an emerging topic among an interdisciplinary community of researchers. This book is aimed at postgraduate and beginning level research scholars who would like to work in the field of Fractional Order Signal processing (FOSP). The readers should have preliminary knowledge about basic signal processing techniques. Prerequisite knowledge of fractional calculus is not essential and is exposited at relevant places in connection to the appropriate signal processing topics. Basic signal processing techniques like filtering, estimation, system identification, etc. in the light of fractional order calculus are presented along with relevant application areas. The readers can easily extend these concepts to varied disciplines like image or speech processing, pattern recognition, time series forecasting, financial data analysis and modeling, traffic modeling in communication channels, optics, biomedical signal processing, electrochemical applications and many more. Adequate references are provided in each category so that the researchers can delve deeper into each area and broaden their horizon of understanding. Available MATLAB tools to simulate FOSP theories are also introduced so that the readers can apply the theoretical concepts right-away and gain practical insight in the specific domain.$

جزئیات و درخواست

By Saptarshi Das, Indranil Pan
Publisher: Springer Science & Business Media, 2011-09-15
Pages: 110
Language: en
ISBN_13:9783642231179
ISBN_10:3642231179
Subject: Technology & Engineering

Advanced Numerical Methods for Differential Equations

Applications in Science and Engineering

جزئیات و درخواست

By Harendra Singh, Jagdev Singh, Sunil Dutt Purohit, Devendra Kumar
Publisher: CRC Press, 2021-07-29
Pages: 337
Language: en
ISBN_13:9781000381085
ISBN_10:1000381080
Subject: Technology & Engineering

Functional and Impulsive Differential Equations of Fractional Order

Qualitative Analysis and Applications

$The book presents qualitative results for different classes of fractional equations, including fractional functional differential equations, fractional impulsive differential equations, and fractional impulsive functional differential equations, which have not been covered by other books. It manifests different constructive methods by demonstrating how these techniques can be applied to investigate qualitative properties of the solutions of fractional systems. Since many applications have been included, the demonstrated techniques and models can be used in training students in mathematical modeling and in the study and development of fractional-order models.$

جزئیات و درخواست

By Ivanka Stamova, Gani Stamov
Publisher: CRC Press, 2017-03-03
Pages: 277
Language: en
ISBN_13:9781498764841
ISBN_10:1498764843
Subject: Mathematics

Analog/Digital Implementation of Fractional Order Chaotic Circuits and Applications

$This book details the simulation and optimization of integer and fractional-order chaotic systems, and how they can be implemented in the analog and digital domains using FPAAs and FPGAs. Design guidelines are provided to use commercially available electronic devices, and to perform hardware descriptions of integer/fractional-order chaotic systems programming in VHDL. Finally, several engineering applications oriented to cryptography, internet of things, robotics and chaotic communications, are detailed to highlight the usefulness of FPAA/FPGA based integer/fractional-order chaotic systems. Provides guidelines to implement fractional-order derivatives using commercially available devices; Describes details on using FPAAs to approach fractional-order chaotic systems; Includes details on using FPGAs to approach fractional-order chaotic systems, programming in VHDL and reducing hardware resources; Discusses applications to cryptography, internet of things, robotics and chaotic communications.$

جزئیات و درخواست

By Esteban Tlelo-Cuautle, Ana Dalia Pano-Azucena, Omar Guillén-Fernández, Alejandro Silva-Juárez
Publisher: Springer Nature, 2019-11-11
Pages: 223
Language: en
ISBN_13:9783030312503
ISBN_10:303031250X
Subject: Technology & Engineering

Intelligent Computations: Abstract Fractional Calculus, Inequalities, Approximations

$This brief book presents the strong fractional analysis of Banach space valued functions of a real domain. The book’s results are abstract in nature: analytic inequalities, Korovkin approximation of functions and neural network approximation. The chapters are self-contained and can be read independently. This concise book is suitable for use in related graduate classes and many research projects. An extensive list of references is provided for each chapter. The book’s results are relevant for many areas of pure and applied mathematics. As such, it offers a unique resource for researchers, and a valuable addition to all science and engineering libraries.$

جزئیات و درخواست

By George A. Anastassiou
Publisher: Springer, 2017-09-02
Pages: 322
Language: en
ISBN_13:9783319669366
ISBN_10:3319669362
Subject: Technology & Engineering

Fractional Calculus View of Complexity

Tomorrow's Science

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

جزئیات و درخواست

By Bruce J. West
Publisher: CRC Press, 2016-01-05
Pages: 304
Language: en
ISBN_13:9781498738019
ISBN_10:149873801X
Subject: Mathematics

Fractional Dynamics on Networks and Lattices

$This book analyzes stochastic processes on networks and regular structures such as lattices by employing the Markovian random walk approach. Part 1 is devoted to the study of local and non-local random walks. It shows how non-local random walk strategies can be defined by functions of the Laplacian matrix that maintain the stochasticity of the transition probabilities. A major result is that only two types of functions are admissible: type (i) functions generate asymptotically local walks with the emergence of Brownian motion, whereas type (ii) functions generate asymptotically scale-free non-local “fractional” walks with the emergence of Lévy flights. In Part 2, fractional dynamics and Lévy flight behavior are analyzed thoroughly, and a generalization of Pólya's classical recurrence theorem is developed for fractional walks. The authors analyze primary fractional walk characteristics such as the mean occupation time, the mean first passage time, the fractal scaling of the set of distinct nodes visited, etc. The results show the improved search capacities of fractional dynamics on networks.$

جزئیات و درخواست

By Thomas Michelitsch, Alejandro Perez Riascos, Bernard Collet, Andrzej Nowakowski, Franck Nicolleau
Publisher: John Wiley & Sons, 2019-04-30
Pages: 340
Language: en
ISBN_13:9781786301581
ISBN_10:178630158X
Subject: Technology & Engineering

Transmutations, Singular and Fractional Differential Equations with Applications to Mathematical Physics

جزئیات و درخواست

By Elina Shishkina, Sergei Sitnik
Publisher: Academic Press, 2020-07-24
Pages: 592
Language: en
ISBN_13:9780128197813
ISBN_10:0128197811
Subject: Mathematics

The Fractional Laplacian

$The fractional Laplacian, also called the Riesz fractional derivative, describes an unusual diffusion process associated with random excursions. The Fractional Laplacian explores applications of the fractional Laplacian in science, engineering, and other areas where long-range interactions and conceptual or physical particle jumps resulting in an irregular diffusive or conductive flux are encountered. Presents the material at a level suitable for a broad audience of scientists and engineers with rudimentary background in ordinary differential equations and integral calculus Clarifies the concept of the fractional Laplacian for functions in one, two, three, or an arbitrary number of dimensions defined over the entire space, satisfying periodicity conditions, or restricted to a finite domain Covers physical and mathematical concepts as well as detailed mathematical derivations Develops a numerical framework for solving differential equations involving the fractional Laplacian and presents specific algorithms accompanied by numerical results in one, two, and three dimensions Discusses viscous flow and physical examples from scientific and engineering disciplines Written by a prolific author well known for his contributions in fluid mechanics, biomechanics, applied mathematics, scientific computing, and computer science, the book emphasizes fundamental ideas and practical numerical computation. It includes original material and novel numerical methods.$

جزئیات و درخواست

By C. Pozrikidis
Publisher: CRC Press, 2018-09-03
Pages: 295
Language: en
ISBN_13:9781315362083
ISBN_10:1315362082
Subject: Mathematics

Fractional Calculus with its Applications in Engineering and Technology

$This book aims to provide the basic theory of fractional calculus and its applications based on practical schemes and approaches, illustrated with applicable engineering and technical examples, especially focusing on the fractional-order controller design. In the development of this book, the essential theorems and facts in the first two chapters are proven with rigorous mathematical analyses. In addition, the commonly used definitions of Grünwald-Letnikov, Riemann-Liouville, Caputo, and Miller-Ross fractional derivatives are introduced with their properties proved and linked to fractional-order controller design. The last chapter presents several enlightening scenarios of fractional-order control designs, for example, the suppression of machining chatter, the nonlinear motion control of a multilink robot, the simultaneous tracking and stabilization control of a rotary inverted pendulum, and the idle speed control of an internal combustion engine (ICE).$

جزئیات و درخواست

By Yi Yang, Haiyan Henry Zhang
Publisher: Springer Nature, 2022-05-31
Pages: 103
Language: en
ISBN_13:9783031796258
ISBN_10:303179625X
Subject: Technology & Engineering

Discrete and Fractional Programming Techniques for Location Models

$At first sight discrete and fractional programming techniques appear to be two com pletely unrelated fields in operations research. We will show how techniques in both fields can be applied separately and in a combined form to particular models in location analysis. Location analysis deals with the problem of deciding where to locate facilities, con sidering the clients to be served, in such a way that a certain criterion is optimized. The term "facilities" immediately suggests factories, warehouses, schools, etc. , while the term "clients" refers to depots, retail units, students, etc. Three basic classes can be identified in location analysis: continuous location, network location and dis crete location. The differences between these fields arise from the structure of the set of possible locations for the facilities. Hence, locating facilities in the plane or in another continuous space corresponds to a continuous location model while finding optimal facility locations on the edges or vertices of a network corresponds to a net work location model. Finally, if the possible set of locations is a finite set of points we have a discrete location model. Each of these fields has been actively studied, arousing intense discussion on the advantages and disadvantages of each of them. The usual requirement that every point in the plane or on the network must be a candidate location point, is one of the mostly used arguments "against" continuous and network location models.$

جزئیات و درخواست

By A. I. Barros
Publisher: Springer Science & Business Media, 1998-04-30
Pages: 210
Language: en
ISBN_10:0792350022
ISBN_13:9780792350026
Subject: Mathematics

Delay Differential Equations and Applications to Biology

$This book discusses the numerical treatment of delay differential equations and their applications in bioscience. A wide range of delay differential equations are discussed with integer and fractional-order derivatives to demonstrate their richer mathematical framework compared to differential equations without memory for the analysis of dynamical systems. The book also provides interesting applications of delay differential equations in infectious diseases, including COVID-19. It will be valuable to mathematicians and specialists associated with mathematical biology, mathematical modelling, life sciences, immunology and infectious diseases.$

جزئیات و درخواست

By Fathalla A. Rihan
Publisher: Springer Nature, 2021-08-19
Pages: 292
Language: en
ISBN_13:9789811606267
ISBN_10:9811606269
Subject: Mathematics

Fractional Statistics and Quantum Theory

$This book explains the subtleties of quantum statistical mechanics in lower dimensions and their possible ramifications in quantum theory. The discussion is at a pedagogical level and is addressed to both graduate students and advanced researchers with a reasonable background in quantum and statistical mechanics. Topics in the first part of the book include the flux tube model of anyons, the braid group and a detailed discussion about the various aspects of quantum and statistical mechanics of a noninteracting anyon gas. The second part of the book includes a detailed discussion about fractional statistics from the point of view of ChernOCoSimons theories. Topics covered here include ChernOCoSimons field theories, charged vortices, anyon superconductivity and the fractional quantum Hall effect. Since the publication of the first edition of the book, an exciting possibility has emerged, that of quantum computing using anyons. A section has therefore been included on this topic in the second edition. In addition, new sections have been added about scattering of anyons with hard disk repulsion as well as fractional exclusion statistics and negative probabilities."$

جزئیات و درخواست

By Avinash Khare
Publisher: World Scientific, 2005
Pages: 316
Language: en
ISBN_13:9789812567758
ISBN_10:9812567755
Subject: Science

Nonlinear, Nonlocal and Fractional Turbulence

Alternative Recipes for the Modeling of Turbulence

$Experts of fluid dynamics agree that turbulence is nonlinear and nonlocal. Because of a direct correspondence, nonlocality also implies fractionality. Fractional dynamics is the physics related to fractal (geometrical) systems and is described by fractional calculus. Up-to-present, numerous criticisms of linear and local theories of turbulence have been published. Nonlinearity has established itself quite well, but so far only a very small number of general nonlocal concepts and no concrete nonlocal turbulent flow solutions were available. This book presents the first analytical and numerical solutions of elementary turbulent flow problems, mainly based on a nonlocal closure. Considerations involve anomalous diffusion (Lévy flights), fractal geometry (fractal-β, bi-fractal and multi-fractal model) and fractional dynamics. Examples include a new ‘law of the wall’ and a generalization of Kraichnan’s energy-enstrophy spectrum that is in harmony with non-extensive and non-equilibrium thermodynamics (Tsallis thermodynamics) and experiments. Furthermore, the presented theories of turbulence reveal critical and cooperative phenomena in analogy with phase transitions in other physical systems, e.g., binary fluids, para-ferromagnetic materials, etc.; the two phases of turbulence identifying the laminar streaks and coherent vorticity-rich structures. This book is intended, apart from fluids specialists, for researchers in physics, as well as applied and numerical mathematics, who would like to acquire knowledge about alternative approaches involved in the analytical and numerical treatment of turbulence.$

جزئیات و درخواست

By Peter William Egolf, Kolumban Hutter
Publisher: Springer Nature, 2020-04-02
Pages: 487
Language: en
ISBN_13:9783030260330
ISBN_10:303026033X
Subject: Science

Time-Fractional Order Biological Systems with Uncertain Parameters

$The subject of fractional calculus has gained considerable popularity and importance during the past three decades, mainly due to its validated applications in various fields of science and engineering. It is a generalization of ordinary differentiation and integration to arbitrary (non-integer) order. The fractional derivative has been used in various physical problems, such as frequency-dependent damping behavior of structures, biological systems, motion of a plate in a Newtonian fluid, PIλDμ controller for the control of dynamical systems, and so on. It is challenging to obtain the solution (both analytical and numerical) of related nonlinear partial differential equations of fractional order. So for the last few decades, a great deal of attention has been directed towards the solution for these kind of problems. Different methods have been developed by other researchers to analyze the above problems with respect to crisp (exact) parameters. However, in real-life applications such as for biological problems, it is not always possible to get exact values of the associated parameters due to errors in measurements/experiments, observations, and many other errors. Therefore, the associated parameters and variables may be considered uncertain. Here, the uncertainties are considered interval/fuzzy. Therefore, the development of appropriate efficient methods and their use in solving the mentioned uncertain problems are the recent challenge. In view of the above, this book is a new attempt to rigorously present a variety of fuzzy (and interval) time-fractional dynamical models with respect to different biological systems using computationally efficient method. The authors believe this book will be helpful to undergraduates, graduates, researchers, industry, faculties, and others throughout the globe.$

جزئیات و درخواست

By Snehashish Chakraverty, Rajarama Mohan Jena, Subrat Kumar Jena
Publisher: Morgan & Claypool Publishers, 2020-03-18
Pages: 162
Language: en
ISBN_13:9781681737508
ISBN_10:1681737507
Subject: Mathematics

Fractional Order Processes

Simulation, Identification, and Control

$The book presents efficient numerical methods for simulation and analysis of physical processes exhibiting fractional order (FO) dynamics. The book introduces FO system identification method to estimate parameters of a mathematical model under consideration from experimental or simulated data. A simple tuning technique, which aims to produce a robust FO PID controller exhibiting iso-damping property during re-parameterization of a plant, is devised in the book. A new numerical method to find an equivalent finite dimensional integer order system for an infinite dimensional FO system is developed in the book. The book also introduces a numerical method to solve FO optimal control problems. Key features Proposes generalized triangular function operational matrices. Shows significant applications of triangular orthogonal functions as well as triangular strip operational matrices in simulation, identification and control of fractional order processes. Provides numerical methods for simulation of physical problems involving different types of weakly singular integral equations, Abel’s integral equation, fractional order integro-differential equations, fractional order differential and differential-algebraic equations, and fractional order partial differential equations. Suggests alternative way to do numerical computation of fractional order signals and systems and control. Provides source codes developed in MATLAB for each chapter, allowing the interested reader to take advantage of these codes for broadening and enhancing the scope of the book itself and developing new results.$

جزئیات و درخواست

By Seshu Kumar Damarla, Madhusree Kundu
Publisher: CRC Press, 2018-09-03
Pages: 263
Language: en
ISBN_13:9780429996887
ISBN_10:0429996888
Subject: Mathematics

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