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Fractional Signals and Systems
-
Manuel Duarte Ortigueira
Language:
English
Published/Copyright:
2020
About this book
The book illustrates the theoretical results of fractional derivatives via applications in signals and systems, covering continuous and discrete derivatives, and the corresponding linear systems. Both time and frequency analysis are presented. Some advanced topics are included like derivatives of stochastic processes. It is an essential reference for researchers in mathematics, physics, and engineering.
- Presents the theory and applications of fractional derivatives in signals and systems.
- Both time and frequency analysis are presented.
- Of interest to mathematicians and physicists as well as to engineers.
Author / Editor information
Manuel Duarte Ortigueira, Universidade Nova de Lisboa, Portugal; Duarte Valério, Instituto Superior Técnico, Portugal.
Topics
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Frontmatter
I -
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Acknowledgement
VII -
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Preface
IX -
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Contents
XI -
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Fractional Calculus in Applied Sciences and Engineering
XVII - Part I: Continuous-time
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1 Introduction to signals and systems
3 -
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2 Continuous-time linear systems and the Laplace transform
21 -
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3 Fractional commensurate linear systems: time responses
39 -
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4 The fractional commensurate linear systems. Frequency responses
61 -
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5 State-space representation
87 -
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6 Feedback representation
95 -
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7 On fractional derivatives
105 - Part II: Discrete-time
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8 Discrete-time linear systems. Difference equations
119 -
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9 Z transform. Transient responses
131 -
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10 Discrete-time derivatives and transforms
163 - Part III: Advanced topics
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11 Fractional stochastic processes and two-sided derivatives
197 -
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12 Fractional delay discrete-time linear systems
213 -
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13 Fractional derivatives with variable orders
221 - Appendices
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A On distributions
237 -
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B The Gamma function and binomial coefficients
240 -
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C The continuous-Time Fourier Transform
243 -
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D The discrete-time Fourier Transform
247 -
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E Partial fraction decomposition without derivations
252 -
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F The Mittag-Leffler function
258 -
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Bibliography
267 -
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Further Reading
273 -
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Index
279 -
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Erratum to: 7 On fractional derivatives
283
Publishing information
Pages and Images/Illustrations in book
eBook published on:
March 9, 2020
eBook ISBN:
9783110624588
Hardcover published on:
March 9, 2020
Hardcover ISBN:
9783110621297
Paperback published on:
January 31, 2022
Paperback ISBN:
9783110777161
Pages and Images/Illustrations in book
Front matter:
17
Main content:
281
Illustrations:
50
Tables:
30
eBook ISBN:
9783110624588
Hardcover ISBN:
9783110621297
Paperback ISBN:
9783110777161
Audience(s) for this book
Applied mathematicians, statistical physicists, computer scientists, and engineers
Safety & product resources
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Manufacturer information:
Walter de Gruyter GmbH
Genthiner Straße 13
10785 Berlin
productsafety@degruyterbrill.com
