Fractional Signals and Systems / / Manuel Duarte Ortigueira, Duarte Valério.

• Superior document: Title is part of eBook package: De Gruyter DG Ebook Package English 2020
• VerfasserIn: Ortigueira, Manuel Duarte,; Valério, Duarte,
• MitwirkendeR: Ortigueira, Manuel D.,; Valério, Duarte,
• Place / Publishing House: Berlin ;, Boston : : De Gruyter, , [2020]; ©2020
• Year of Publication: 2020
• Language: English
• Series: Fractional Calculus in Applied Sciences and Engineering , 7
• Physical Description: 1 online resource (XVII, 281 p.)
• Other title: Frontmatter --; Acknowledgement --; Preface --; Contents --; Fractional Calculus in Applied Sciences and Engineering --; Part I: Continuous-time --; 1 Introduction to signals and systems --; 2 Continuous-time linear systems and the Laplace transform --; 3 Fractional commensurate linear systems: time responses --; 4 The fractional commensurate linear systems. Frequency responses --; 5 State-space representation --; 6 Feedback representation --; 7 On fractional derivatives --; Part II: Discrete-time --; 8 Discrete-time linear systems. Difference equations --; 9 Z transform. Transient responses --; 10 Discrete-time derivatives and transforms --; Part III: Advanced topics --; 11 Fractional stochastic processes and two-sided derivatives --; 12 Fractional delay discrete-time linear systems --; 13 Fractional derivatives with variable orders --; Appendices --; A On distributions --; B The Gamma function and binomial coefficients --; C The continuous-Time Fourier Transform --; D The discrete-time Fourier Transform --; E Partial fraction decomposition without derivations --; F The Mittag-Leffler function --; Bibliography --; Further Reading --; Index --; Erratum to: 7 On fractional derivatives
• Format: Mode of access: Internet via World Wide Web.
• ISBN: 9783110624588; 9783110696288; 9783110696271; 9783110659061; 9783110704716; 9783110704518; 9783110704846; 9783110704662
• ISSN: 2509-7210
• DOI: 10.1515/9783110624588
• Access: restricted access
• Hierarchical level: Monograph
• Statement of Responsibility: Manuel Duarte Ortigueira, Duarte Valério.

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.