Functional Fractional Calculus [recurso electrónico] / by Shantanu Das.

Por: Das, Shantanu [author.]Colaborador(es): SpringerLink (Online service)Tipo de material: TextoTextoEditor: Berlin, Heidelberg : Springer Berlin Heidelberg, 2011Descripción: XXVIII, 612 p. online resourceTipo de contenido: text Tipo de medio: computer Tipo de portador: online resourceISBN: 9783642205453Tema(s): Engineering | Computer science | Physics | Engineering mathematics | Engineering | Appl.Mathematics/Computational Methods of Engineering | Computational Science and Engineering | ComplexityFormatos físicos adicionales: Printed edition:: Sin títuloClasificación CDD: 519 Clasificación LoC:TA329-348TA640-643Recursos en línea: Libro electrónicoTexto
Contenidos:
CHAPTER 1 INTRODUCTION TO FRACTIONAL CALCULUS --   CHAPTER 2FUNCTIONS USED IN FRACTIONAL CALCULUS --   CHAPTER 3   OBSERVATION OF FRACTIONAL CALCULUS IN PHYSICAL SYSTEM DESCRIPTION --     CHAPTER-4   CONCEPT OF FRACTIONAL DIVERGENCE AND FRACTIONAL CURL CHAPTER-5 --   FRACTIONAL DIFFERINTEGRATIONS INSIGHT CONCEPTS -- CHAPTER-6   INITIALIZED DIFFERINTEGRALS AND GENERALIZED CALCULUS --   CHAPTER-7   GENERALIZED LAPLACE TRANSFORM FOR FRACTIONAL DIFFERINTEGRALS -- CHAPTER-8   APPLICATION OF GENERALIZED FRACTIONAL CALCULUS IN ELECTRICAL CIRCUIT ANALYSIS & ELECTROMAGNETICS --   CHAPTER-9   APPLICATION OF GENERALIZED FRACTIONAL CALCULUS IN OTHER SCIENCE AND ENGINEERING FIELDS --   CHAPTER-10   SYSTEM ORDER IDENTIFICATION AND CONTROL --   CHAPTER-11   SOLUTION OF GENERALIZED DIFFERENTIAL EQUATION SYSTEMS .
En: Springer eBooksResumen: When a new extraordinary and outstanding theory is stated, it has to face criticism and skeptism, because it is beyond the usual concept. The fractional calculus though not new, was not discussed or developed for a long time, particularly for lack of its application to real life problems. It is extraordinary because it does not deal with ‘ordinary’ differential calculus. It is outstanding because it can now be applied to situations where existing theories fail to give satisfactory results. In this book not only mathematical abstractions are discussed in a lucid manner, with physical mathematical and geometrical explanations, but also several practical applications are given particularly for system identification, description and then efficient controls. In the second edition of this successful book the concepts of fractional and complex order differentiation and integration are elaborated mathematically, physically and geometrically. Various important new examples are presented, such as heterogeneity effects in transport background, the space having traps or islands, irregular distribution of charges, non-ideal spring with mass connected to a pointless-mass ball, material behaving with viscous as well as elastic properties, system relaxation with and without memory, or physics of random delay in computer networks . Special emphasis in this new edition is placed on the practical utility of local fractional differentiation for enhancing the character of singularity at phase transition or characterizing the irregularity measure of response function. Practical results of viscoelastic experiments, fractional order control experiments, design of fractional controller and practical circuit synthesis for fractional order elements are presented in a modern approach as well.
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Existencias
Tipo de ítem Biblioteca actual Colección Signatura Copia número Estado Fecha de vencimiento Código de barras
Libro Electrónico Biblioteca Electrónica
Colección de Libros Electrónicos TA329 -348 (Browse shelf(Abre debajo)) 1 No para préstamo 376102-2001

CHAPTER 1 INTRODUCTION TO FRACTIONAL CALCULUS --   CHAPTER 2FUNCTIONS USED IN FRACTIONAL CALCULUS --   CHAPTER 3   OBSERVATION OF FRACTIONAL CALCULUS IN PHYSICAL SYSTEM DESCRIPTION --     CHAPTER-4   CONCEPT OF FRACTIONAL DIVERGENCE AND FRACTIONAL CURL CHAPTER-5 --   FRACTIONAL DIFFERINTEGRATIONS INSIGHT CONCEPTS -- CHAPTER-6   INITIALIZED DIFFERINTEGRALS AND GENERALIZED CALCULUS --   CHAPTER-7   GENERALIZED LAPLACE TRANSFORM FOR FRACTIONAL DIFFERINTEGRALS -- CHAPTER-8   APPLICATION OF GENERALIZED FRACTIONAL CALCULUS IN ELECTRICAL CIRCUIT ANALYSIS & ELECTROMAGNETICS --   CHAPTER-9   APPLICATION OF GENERALIZED FRACTIONAL CALCULUS IN OTHER SCIENCE AND ENGINEERING FIELDS --   CHAPTER-10   SYSTEM ORDER IDENTIFICATION AND CONTROL --   CHAPTER-11   SOLUTION OF GENERALIZED DIFFERENTIAL EQUATION SYSTEMS .

When a new extraordinary and outstanding theory is stated, it has to face criticism and skeptism, because it is beyond the usual concept. The fractional calculus though not new, was not discussed or developed for a long time, particularly for lack of its application to real life problems. It is extraordinary because it does not deal with ‘ordinary’ differential calculus. It is outstanding because it can now be applied to situations where existing theories fail to give satisfactory results. In this book not only mathematical abstractions are discussed in a lucid manner, with physical mathematical and geometrical explanations, but also several practical applications are given particularly for system identification, description and then efficient controls. In the second edition of this successful book the concepts of fractional and complex order differentiation and integration are elaborated mathematically, physically and geometrically. Various important new examples are presented, such as heterogeneity effects in transport background, the space having traps or islands, irregular distribution of charges, non-ideal spring with mass connected to a pointless-mass ball, material behaving with viscous as well as elastic properties, system relaxation with and without memory, or physics of random delay in computer networks . Special emphasis in this new edition is placed on the practical utility of local fractional differentiation for enhancing the character of singularity at phase transition or characterizing the irregularity measure of response function. Practical results of viscoelastic experiments, fractional order control experiments, design of fractional controller and practical circuit synthesis for fractional order elements are presented in a modern approach as well.

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