Fractional Differential Equations: An Introduction to Fractional Derivatives, Fractional Differential Equations, to Methods of Their Solution and Some of Their ApplicationsElsevier, 27. 10. 1998 - 340 strán (strany) 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. - A unique survey of many applications of fractional calculus - Presents basic theory - Includes a unified presentation of selected classical results, which are important for applications - Provides many examples - Contains a separate chapter of fractional order control systems, which opens new perspectives in control theory - The first systematic consideration of Caputo's fractional derivative in comparison with other selected approaches - Includes tables of fractional derivatives, which can be used for evaluation of all considered types of fractional derivatives |
Obsah
| 1 | |
Chapter 2 Fractional Derivatives and Integrals | 41 |
Chapter 3 Existence and Uniqueness Theorems | 121 |
Chapter 4 The Laplace Transform Method | 137 |
Chapter 5 Fractional Greens Function | 149 |
Chapter 6 Other Methods for the Solution of Fractionalorder Equations | 159 |
Chapter 7 Numerical Evaluation of Fractional Derivatives | 199 |
Chapter 8 Numerical Solution of Fractional Differential Equations | 223 |
Chapter 9 Fractionalorder Systems and Controllers | 243 |
Chapter 10 Survey of Applications of the Fractional Calculus | 261 |
Tables of Fractional Derivatives | 309 |
| 313 | |
| 337 | |
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Časté výrazy a frázy
aDif(t applied problems approach approximation beta function Chapter classical computations constant coefficients contour denote derivative of order described equations with constant evaluation example expression finite-part integrals fluid formula Fourier transform frac fractional calculus fractional differential equations fractional Green's function fractional integral fractional-order controlled fractional-order models fractional-order system function f(t gamma function gives Grünwald-Letnikov initial conditions initial value problem initial-value problem integer-order derivatives integer-order models integral equation inverse Laplace transform Jacobi polynomials Let us consider Letnikov linear fractional differential Liouville Liouville fractional lower terminal mathematical Mellin transform memory length Miller-Ross Mittag-Leffler function Newtonian fluid non-integer numerical solution obtain orthogonal polynomials parameters power series properties Re(z real number Riemann Riemann-Liouville fractional derivative Section sequential fractional derivatives spectral relationship Taking into account Theorem theory tion tional derivative transfer function unit-step response viscoelasticity