An Introduction to Fractional Derivatives, Fractional Differential Equations, to Methods of Their Solution and Some of Their Applications To order this title, and for more information, click here
By Igor Podlubny, Technical University of Kosice, Slovak Republic
Description This book is a landmark title in the continuous move from integer to non-integer in mathematics: from integer numbers to real numbers,
from factorials to the gamma function, from integer-order models to models of an arbitrary order. For historical reasons, the word 'fractional'
is used instead of the word 'arbitrary'.
This book is written for readers who are new to the fields of fractional derivatives and fractional-order
mathematical models, and feel that they need them for developing more adequate mathematical models.
In this book, not only applied scientists,
but also pure mathematicians will find fresh motivation for developing new methods and approaches in their fields of research.
A reader
will find in this book everything necessary for the initial study and immediate application of fractional derivatives fractional differential
equations, including several necessary special functions, basic theory of fractional differentiation, uniqueness and existence theorems,
analytical numerical methods of solution of fractional differential equations, and many inspiring examples of applications.
Audience
Researchers in math analysis; engineers; mathematicians; applied scientists wishing to use fractional-order models for modeling and studying
processes in a particular field; teachers and students of differential and integral calculus, and mathematical and theoretical physics.
Contents Preface. Acknowledgments.
Special Functions Of Preface. Acknowledgements. Special Functions of the Fractional Calculus .
Gamma Function. Mittag-Leffler Function. Wright Function.
Fractional Derivatives and Integrals . The Name of the Game.
Grunwald-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 Theorems . 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 Method . Standard Fractional Differential Equations.
Sequential Fractional Differential Equations.
Fractional Green's Function . 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: n-term Equation.
Other Methods for the Solution of Fractional-order
Equations . The Mellin Transform Method. Power Series Method. Babenko's Symbolic Calculus Method. Method of Orthogonal Polynomials.
Numerical Evaluation of Fractional Derivatives . Approximation of Fractional Derivatives. The "Short-Memory" Principle.
Order of Approximation. Computation of Coefficients. Higher-order Approximations.
Numerical Solution of Fractional Differential
Equations . 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 Controllers . 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.
Books and book related electronic products are priced in US dollars (USD), euro (EUR), and Great Britain Pounds (GBP). USD prices apply to the Americas and Asia Pacific. EUR prices apply in Europe and the Middle East. GBP prices apply to the UK and all other countries.
Home | Elsevier Sites | Privacy Policy | Terms and Conditions | Feedback | Site Map | A Reed Elsevier Company