| Description |
1 online resource (xxiv, 340 pages) : illustrations. |
| Physical Medium |
polychrome |
| Description |
text file |
| Series |
Mathematics in science and engineering ; v. 198
|
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Mathematics in science and engineering ; v. 198.
|
| Bibliography |
Includes bibliographical references (pages 313-335) and index. |
| Summary |
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. Key Features * 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. |
| 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. Grünwald-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. Tables of Fractional Derivatives. Index. |
| Local Note |
eBooks on EBSCOhost EBSCO eBook Subscription Academic Collection - North America |
| Subject |
Differential equations -- Numerical solutions.
|
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Differential equations -- Numerical solutions. |
|
Fractional calculus.
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Fractional calculus. |
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Differential equations.
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Differential equations. |
| Genre/Form |
Electronic books.
|
| Other Form: |
Print version: Podlubny, Ogor. Fractional differential equations : an introduction to fractional derivatives, fractional differential equations, to methods of their solution and some of their applications. San Diego : Academic Press, 1999 0125588402 9780125588409 (DLC) 2008297489 (OCoLC)40225390 |
| ISBN |
9780080531984 (electronic book) |
|
0080531989 (electronic book) |
|
0125588402 |
|
9780125588409 |
|
9780125588409 |
|
