Introduction to Fractional and Pseudo-Differential Equations with Singular Symbols
Nonfiction, Science & Nature, Mathematics, Differential Equations, Statistics
| Author: | Sabir Umarov | ISBN: | 9783319207711 |
| Publisher: | Springer International Publishing | Publication: | August 18, 2015 |
| Imprint: | Springer | Language: | English |
| Author: | Sabir Umarov |
| ISBN: | 9783319207711 |
| Publisher: | Springer International Publishing |
| Publication: | August 18, 2015 |
| Imprint: | Springer |
| Language: | English |
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.
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.
