Introduction to fractional and pseudo-differential equations with singular symbols
Sabir Umarov (Author)
The book systematically presents the theories of pseudo-differential operators with symbols singular in dual variables, fractional order derivatives, distributed and variable order fractional derivatives, random walk approximants, and applications of these theories to various initial and multi-point boundary value problems for pseudo-differential equations. Fractional Fokker-Planck-Kolmogorov equations associated with a large class of stochastic processes are presented. A complex version of the theory of pseudo-differential operators with meromorphic symbols based on the recently introduced complex Fourier transform is developed and applied for initial and boundary value problems for systems of complex differential and pseudo-differential equations
Developments in mathematics, v. 41, volume 41
xvi, 434 pages ; 24 cm.
9783319207704, 9783319207711, 3319207709, 3319207717
910412110
1. Function spaces and distributions
2. Pseudo-differential operators with singular symbols (DOSS)
3. Fractional calculus and fractional order operators
4. Boundary value problems for pseudo-differential equations with singular symbols
5. Initial and boundary value problems for fractional order differential equations
6. Distributed and variable order differential-operator equations
7. Fractional order Fokker-Planck-Kolmogorov equations and associated stochastic processes
8. Random walk approximants of mixed and time-changed Lévy processes
9. Complex DOSS and systems of complex differential equations