Mittag-Leffler function: properties and applications

Kapitel in diesem Buch

1. Frontmatter I
2. Preface V
3. Contents VII
4. Recent history of the fractional calculus: data and statistics 1
5. Basic FC operators and their properties 23
6. Mathematical and physical interpretations of fractional derivatives and integrals 47
7. Generalized fractional calculus operators with special functions 87
8. General fractional calculus 111
9. Multiple Erdélyi–Kober integrals and derivatives as operators of generalized fractional calculus 127
10. Fractional Laplace operator and its properties 159
11. Applications of the Mellin integral transform technique in fractional calculus 195
12. Fractional Fourier transform 225
13. The Wright function and its applications 241
14. Mittag-Leffler function: properties and applications 269
15. Asymptotics of the special functions of fractional calculus 297
16. Analysis of fractional integro-differential equations of thermistor type 327
17. A survey on fractional variational calculus 347
18. Variational principles with fractional derivatives 361
19. Continuous time random walks and space-time fractional differential equations 385
20. Inverse subordinators and time fractional equations 407
21. Spectral theory of fractional order integration operators, their direct sums, and similarity problem to these operators of their weak perturbations 427
22. Fractional differentiation in p-adic analysis 461
23. Index 473