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Functional Fractional Calculus

Functional Fractional Calculus
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Feldname Details
Vorliegende Sprache eng
Hinweise auf parallele Ausgaben 34747487X Buchausg. u.d.T.: ‡Das, Shantanu: Functional fractional calculus
ISBN 978-3-642-20544-6
Name Das, Shantanu
T I T E L Functional Fractional Calculus
Verlagsort Berlin, Heidelberg
Verlag Springer-Verlag Berlin Heidelberg
Erscheinungsjahr 2011
2011
Umfang Online-Ressource (XXVIII, 616p. 108 illus, digital)
Reihe SpringerLink. Bücher
Notiz / Fußnoten Includes bibliographical references
Weiterer Inhalt Title; Preface; Contents; Introduction to Fractional Calculus; Introduction; Birth of Fractional Calculus; Fractional Calculus a Generalization of Integer Order Calculus; Historical Development of Fractional Calculus; About Fractional Integration Derivatives and Differintegration; Solution of Fractional Differential Equations; Conservation of Probability; Half Order Fractional Differentiation Embedded in Standard Fick's Law and Its Extension to Describe Anamolous Diffusion; Fractional Brownian Motion; A Thought Experiment; Quotable Quotes about Fractional Calculus; Concluding Comments. Functions Used in Fractional CalculusIntroduction; Functions for the Fractional Calculus; List of Laplace and Inverse Laplace Transforms Related to Fractional Calculus; Paradoxial Conditions for Using Generalized Differentiation and Integration Expressions and Cautions; Non-exponential Relaxation Power Law and Memory Integrals; Boltzmann's Superposition Principle; Motivation to Use Higher Transcendental Functions to Solve Fractional Differential Equations; Fractional Derivatives and Integrals of Important Functions with Use of Higher Transcendental Functions. Irregular Functions and Measure of Irregularity (Roughness) with Box Dimension, Holder and Hurst's ExponentsConcluding Comments; Observation of Fractional Calculus in Physical System Description; Introduction; Temperature Heat Flux Relationship for Heat Flowing in Semi-infinite Conductor; Single Thermocouple Junction Temperature in Measurement of Heat Flux; Heat Transfer; Driving Point Impedance of Semi-infinite Lossy Transmission Line; Semi Infinite Lossless Transmission Line; Partial Differential Equations and Operational Calculus; Fick's Diffusion Discussion; Cattaneo Diffusion. Anomalous DiffusionTruncation of Semi-Infinite System to a Finite System; Approximating the Half Order by Self Similar Structure and Its Relation to Continued Fraction Expansion; Dynamics of Chain Network; Dynamics of Charged Chain Network in Electric Field; Concluding Comments; Concept of Fractional Divergence and Fractional Curl; Introduction; Concept of Fractional Divergence for Particle Flux; Fractional Kinetic Equation; Discrete Difference and Continuum Limit and Differential Operator in Random Walk Context; Nuclear Reactor Neutron Flux Description. Classical Constitutive Neutron Diffusion EquationDiffusion with Long Jumps; Fractional Divergence in Neutron Diffusion Equations; Concept of Fractional Curl in Electromagnetics; Concluding Comments; Fractional Differintegrations Insight Concepts; Introduction; Calculating Fractional Integral; Fractional Differintegration of Product of Two Functions; Symbol Standardization and Description for Differintegration; Riemann-Liouville Fractional Differintegral; Grunwald-Letnikov Fractional Differinteration; Unification of Differintegration through Binomial Coefficients. Short Memory Principle- A Moving Start Point Approximation and Its Error
Titelhinweis Buchausg. u.d.T.: ‡Das, Shantanu: Functional fractional calculus
ISBN ISBN 978-3-642-20545-3
Klassifikation TBJ
MAT003000
*26A33
00A06
519
515.83
TA329-348
TA640-643
QH 150
Kurzbeschreibung 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 mathematic
1. Schlagwortkette Gebrochene Analysis
1. Schlagwortkette ANZEIGE DER KETTE Gebrochene Analysis
2. Schlagwortkette Gebrochene Analysis
ANZEIGE DER KETTE Gebrochene Analysis
SWB-Titel-Idn 34869637X
Signatur Springer E-Book
Bemerkungen Elektronischer Volltext - Campuslizenz
Elektronische Adresse $uhttp://dx.doi.org/10.1007/978-3-642-20545-3
Internetseite / Link Volltext
Siehe auch Volltext
Siehe auch Cover
Siehe auch Inhaltstext
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