Format:
Online Ressource (xiii, 234 pages)
,
illustrations.
Edition:
Online-Ausg. [S.l.] HathiTrust Digital Library Online-Ausg. [S.l.] : HathiTrust Digital Library
ISBN:
9780080956206
,
0080956203
,
9780125255509
,
9781282702899
Series Statement:
Mathematics in science and engineering v. 111
Content:
In this book, we study theoretical and practical aspects of computing methods for mathematical modelling of nonlinear systems. A number of computing techniques are considered, such as methods of operator approximation with any given accuracy; operator interpolation techniques including a non-Lagrange interpolation; methods of system representation subject to constraints associated with concepts of causality, memory and stationarity; methods of system representation with an accuracy that is the best within a given class of models; methods of covariance matrix estimation;methods for low-rank
Note:
Includes bibliographical references (pages 219-223) and index. - Print version record
,
Print version record
,
Master and use copy. Digital master created according to Benchmark for Faithful Digital Reproductions of Monographs and Serials, Version 1. Digital Library Federation, December 2002
,
Front Cover; THE FRACTIONAL CALCULUS; Copyright Page; CONTENTS; Preface; Acknowledgments; Chapter 1. INTRODUCTION; 1.1 Historical Survey; 1.2 Notation; 1.3 Properties of the Gamma Function; Chapter 2. DIFFERENTIATION AND INTEGRATION TO INTEGER ORDER; 2.1 Symbolism; 2.2 Conventional Definitions; 2.3 Composition Rule for Mixed Integer Orders; 2.4 Dependence of Multiple Integrals on Lower Limit; 2.5 Product Rule for Multiple Integrals; 2.6 The Chain Rule for Multiple Derivatives; 2.7 Iterated Integrals; 2.8 Differentiation and Integration of Series; 2.9 Differentiation and Integration of Powers
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2.10 Differentiation and Integration of HypergeometricsChapter 3. FRACTIONAL DERIVATIVES AND INTEGRALS: DEFINITIONS AND EQUIVALENCES; 3.1 Differintegrable Functions; 3.2 Fundamental Definitions; 3.3 Identity of Definitions; 3.4 Other General Definitions; 3.5 Other Formulas Applicable to Analytic Functions; 3.6 Summary of Definitions; Chapter 4. DIFFERINTEGRATION OF SIMPLE FUNCTlONS; 4.1 The Unit Function; 4.2 The Zero Function; 4.3 The Function x - a; 4.4 The Function [x - a]a; Chapter 5. GENERAL PROPERTIES; 5.1 Linearity; 5.2 Differintegration Term by Term; 5.3 Homogeneity; 5.4 Scale Change
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5.5 Leibniz's Rule5.6 Chain Rule; 5.7 Composition Rule; 5.8 Dependence on Lower Limit; 5.9 Translation; 5.10 Behavior Near Lower Limit; 5.11 Behavior Far from Lower Limit; Chapter 6. DIFFERINTEGRATION OF MORE COMPLEX FUNCTIONS; 6.1 The Binomial Function [C - cx]p; 6.2 The Exponential Function exp(C - cx); 6.3 The Functions xq/[1 - x] and xp/[1 - x] and [1 - X]q-1; 6.4 The Hyperbolic and Trigonometric Functions sinh(vx) and sin (x); 6.5 The Bessel Functions; 6.6 Hypergeometric Functions; 6.7 Logarithms; 6.8 The Heaviside and Dirac Functions; 6.9 The Sawtooth Function; 6.10 Periodic Functions
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6.11 Cyclodifferential Functions6.12 The Function xq - 1 exp[-1/x]; Chapter 7. SEMIDERIVATIVES AND SEMIINTEG RALS; 7.1 Definitions; 7.2 Genera1 Properties; 7.3 Constants and Powers; 7.4 Binomials; 7.5 Exponential and Related Functions; 7.6 Trigonometric and Hyperbolic Functions; 7.7 Bessel and Struve Functions; 7.8 Generalized Hypergeometric Functions; 7.9 Miscellaneous Functions; Chapter 8. TECHNIQUES IN THE FRACTIONAL CALCULUS; 8.1 Laplace Transformation; 8.2 Numerical Differintegration; 8.3 Analog Differintegration; 8.4 Extraordinary Differential Equations; 8.5 Semidifferential Equations
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8.6 Series SolutionsChapter 9. REPRESENTATION OF TRANSCENDENTAL FUNCTIONS; 9.1 Transcendental Functions as Hypergeometrics; 9.2 Hypergeometrics with K 〉 L; 9.3 Reduction of Complex Hypergeometrics; 9.4 Basis Hypergeometrics; 9.5 Synthesis of K = L Transcendentals; 9.6 Synthesis of K = L - 1 Transcendentals; 9.7 Synthesis of K = L - 2 Transcendentals; Chapter 10. APPLICATIONS IN THE CLASSICAL CALCULUS; 10.1 Evaluation of Definite Integrals and Infinite Sums; 10.2 Abel's Integral Equation; 10.3 Solution of Bessel's Equation; 10.4 Candidate Solutions for Differential Equations
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10.5 Function Families
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Online-Ausg. [S.l.] : HathiTrust Digital Library
,
Master and use copy. Digital master created according to Benchmark for Faithful Digital Reproductions of Monographs and Serials, Version 1. Digital Library Federation, December 2002.
Additional Edition:
ISBN 0125255500
Additional Edition:
Erscheint auch als Druck-Ausgabe Oldham, Keith B Fractional calculus New York, Academic Press, 1974
Language:
English
Keywords:
Ableitung gebrochener Ordnung
;
Electronic books
;
Electronic books
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