Introduction to Fractional and Pseudo-Differential Equations with Singular Symbols

• Main Author: Umarov, Sabir (Author)
• Corporate Author: SpringerLink (Online service)
• Format: Electronic eBook
• Language: English
• Published: Cham : Springer International Publishing : Imprint: Springer, 2015.
• Series: Developments in Mathematics, 41
• Subjects: Mathematics.; Fourier analysis.; Partial differential equations.; Probabilities.; Statistical physics.; Dynamical systems.; Partial Differential Equations.; Probability Theory and Stochastic Processes.; Fourier Analysis.; Statistical Physics, Dynamical Systems and Complexity.
• Physical Description: XVI, 434 p. 2 illus. online resource.
• ISBN: 9783319207711
• ISSN: 1389-2177 ;

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.