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book: Fractional Signals and Systems
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Fractional Signals and Systems

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Language: English
Published/Copyright: 2020
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Fractional Calculus in Applied Sciences and Engineering

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
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  • 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
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  • 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
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  • 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
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  • 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
    Manuel D. Ortigueira and Duarte Valério
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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
https://doi.org/10.1515/9783110624588
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
Manufacturer information:
Walter de Gruyter GmbH
Genthiner Straße 13
10785 Berlin
productsafety@degruyterbrill.com
Downloaded on 26.4.2026 from https://www.degruyterbrill.com/document/doi/10.1515/9783110624588/html?lang=en
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