Fractional differential equations : an introduction to fractional derivatives, fractional differential equations, to methods of their solution and some of their applications /

Fractional differential equations : an introduction to fractional derivatives, fractional differential equations, to methods of their solution and some of their applications /

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Bibliographic Details
Author / Creator:Podlubny, Igor.
Imprint:San Diego : Academic Press, c1999.
Description:xxiv, 340 p. : ill. ; 24 cm.
Language:English
Series:Mathematics in science and engineering v. 198
Subject:
Differential equations -- Numerical solutions.
Fractional calculus.
Differential equations -- Numerical solutions.
Fractional calculus.
Format: Print Book
URL for this record:http://pi.lib.uchicago.edu/1001/cat/bib/3509115
Hidden Bibliographic Details
ISBN:0125588402
Notes:Includes bibliographical references (p. 313-335) and index.
Table of Contents:
  • Preface
  • Acknowledgments
  • Special Functions of Preface
  • Acknowledgements
  • Special Functions of the Fractional Calculuslt
  • Gamma Function
  • Mittag-Leffler Function
  • Wright Function
  • Fractional Derivatives and Integralslt
  • The Name of the Game
  • Gruuml;nwald-Letnikov Fractional Derivatives
  • Riemann-Liouville Fractional Derivatives
  • Some Other Approaches
  • Sequential Fractional Derivatives
  • Left and Right Fractional Derivatives
  • Properties of Fractional Derivatives
  • Laplace Transforms of Fractional Derivatives
  • Fourier Transforms of Fractional Derivatives
  • Mellin Transforms of Fractional Derivatives
  • Existence and Uniqueness Theoremslt
  • Linear Fractional Differential Equations
  • Fractional Differential Equation of a General Form
  • Existence and Uniqueness Theorem as a Method of Solution
  • Dependence of a Solution on Initial Conditions
  • The Laplace Transform Methodlt
  • Standard Fractional Differential Equations
  • Sequential Fractional Differential Equations
  • Fractional Green's Functionlt
  • Definition and Some Properties
  • One. Term Equation
  • Two. Term Equation
  • Three. Term Equation.
  • Four. Term Equation
  • Calculation of Heat Load Intensity Change in Blast Furnace Walls
  • Finite-Part Integrals and Fractional Derivatives
  • General Case: nlt;/i> -term Equation
  • Other Methods for the Solution of Fractional-order Equationslt
  • The Mellin Transform Method
  • Power Series Method
  • Babenko's Symbolic Calculus Method
  • Method of Orthogonal Polynomials
  • Numerical Evaluation of Fractional Derivativeslt
  • Approximation of Fractional Derivatives
  • The "Short-Memory" Principle
  • Order of Approximation
  • Computation of Coefficients
  • Higher-order Approximations
  • Numerical Solution of Fractional Differential Equationslt
  • Initial Conditions: Which Problem to Solve? Numerical Solution
  • Examples of Numerical Solutions
  • The "Short-Memory" Principle in Initial Value Problems for Fractional Differential Equations
  • Fractional-Order Systems and Controllers
  • Fractional-Order Systems and Fractional-Order Controllerslt
  • Example
  • on Viscoelasticity
  • Bode's Analysis of Feedback Amplifiers
  • Fractional Capacitor Theory
  • Electrical Circuits
  • Electroanalytical Chemistry
  • Electrode-Electrolyte Interface
  • Fractional Multipoles
  • Biology
  • Fractional Diffusion Equations
  • Control Theory
  • Fitting of Experimental Data
  • The "Fractional-Order" Physics? Bibliography
  • Tables of Fractional Derivativeslt
  • Index

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