Contents

Chapters in this book

1. Frontmatter I
2. Preface V
3. Contents VII
4. General theory of Caputo-type fractional differential equations 1
5. Problems of Sturm–Liouville type for differential equations with fractional derivatives 21
6. Maps with power-law memory: direct introduction and Eulerian numbers, fractional maps, and fractional difference maps 47
7. Symmetries and group invariant solutions of fractional ordinary differential equations 65
8. Operational method for fractional ordinary differential equations 91
9. Lyapunov-type inequalities for fractional boundary value problems 119
10. Fractional-parabolic equations and systems. Cauchy problem 145
11. Time fractional diffusion equations: solution concepts, regularity, and long-time behavior 159
12. Layer potentials for the time-fractional diffusion equation 181
13. Fractional-hyperbolic equations and systems. Cauchy problem 197
14. Equations with general fractional time derivatives–Cauchy problem 223
15. User’s guide to the fractional Laplacian and the method of semigroups 235
16. Parametrix methods for equations with fractional Laplacians 267
17. Maximum principle for the time-fractional PDEs 299
18. Wave equation involving fractional derivatives of real and complex fractional order 327
19. Symmetries, conservation laws and group invariant solutions of fractional PDEs 353
20. Fractional Duhamel principle 383
21. Inverse problems of determining sources of the fractional partial differential equations 411
22. Inverse problems of determining parameters of the fractional partial differential equations 431
23. Inverse problems of determining coefficients of the fractional partial differential equations 443
24. Abstract linear fractional evolution equations 465
25. Abstract nonlinear fractional evolution equations 499
26. Index 515