معادلات دیفرانسیل کسری ۲۰۱۹
Fractional Differential Equations 2019

1. Preface

2. Contents

3. General theory of Caputo-type fractional differential equations

4. Problems of Sturm–Liouville type for differential equations with fractional derivatives

5. Maps with power-law memory: direct introduction and Eulerian numbers, fractional maps, and fractional difference maps

6. Symmetries and group invariant solutions of fractional ordinary differential equations

7. Operational method for fractional ordinary differential equations

8. Lyapunov-type inequalities for fractional boundary value problems

9. Fractional-parabolic equations and systems. Cauchy problem

10. Time fractional diffusion equations: solution concepts, regularity, and long-time behavior

11. Layer potentials for the time-fractional diffusion equation

12. Fractional-hyperbolic equations and systems. Cauchy problem

13. Equations with general fractional time derivatives–Cauchy problem

14. User’s guide to the fractional Laplacian and the method of semigroups

15. Parametrix methods for equations with fractional Laplacians

16. Maximum principle for the time-fractional PDEs

17. Wave equation involving fractional derivatives of real and complex fractional order

18. Symmetries, conservation laws and group invariant solutions of fractional PDEs

19. Fractional Duhamel principle

20. Inverse problems of determining sources of the fractional partial differential equations

21. Inverse problems of determining parameters of the fractional partial differential equations

22. Inverse problems of determining coefficients of the fractional partial differential equations

23. Abstract linear fractional evolution equations

24. Abstract nonlinear fractional evolution equations

25. Index