A On distributions

Chapters in this book

1. Frontmatter I
2. Acknowledgement VII
3. Preface IX
4. Contents XI
5. Fractional Calculus in Applied Sciences and Engineering XVII
6. Part I: Continuous-time
7. 1 Introduction to signals and systems 3
8. 2 Continuous-time linear systems and the Laplace transform 21
9. 3 Fractional commensurate linear systems: time responses 39
10. 4 The fractional commensurate linear systems. Frequency responses 61
11. 5 State-space representation 87
12. 6 Feedback representation 95
13. 7 On fractional derivatives 105
14. Part II: Discrete-time
15. 8 Discrete-time linear systems. Difference equations 119
16. 9 Z transform. Transient responses 131
17. 10 Discrete-time derivatives and transforms 163
18. Part III: Advanced topics
19. 11 Fractional stochastic processes and two-sided derivatives 197
20. 12 Fractional delay discrete-time linear systems 213
21. 13 Fractional derivatives with variable orders 221
22. Appendices
23. A On distributions 237
24. B The Gamma function and binomial coefficients 240
25. C The continuous-Time Fourier Transform 243
26. D The discrete-time Fourier Transform 247
27. E Partial fraction decomposition without derivations 252
28. F The Mittag-Leffler function 258
29. Bibliography 267
30. Further Reading 273
31. Index 279
32. Erratum to: 7 On fractional derivatives 283