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＜電子ブック＞
Introduction to Fractional and Pseudo-Differential Equations with Singular Symbols / by Sabir Umarov
(Developments in Mathematics. ISSN:2197795X ; 41)

版	1st ed. 2015.
出版者	(Cham : Springer International Publishing : Imprint: Springer)
出版年	2015
大きさ	XVI, 434 p. 2 illus : online resource
著者標目	*Umarov, Sabir author SpringerLink (Online service)
件　名	LCSH:Differential equations LCSH:Probabilities LCSH:Fourier analysis LCSH:System theory LCSH:Mathematical physics FREE:Differential Equations FREE:Probability Theory FREE:Fourier Analysis FREE:Complex Systems FREE:Theoretical, Mathematical and Computational Physics
一般注記	Function Spaces and Distributions -- Pseudo-Differential Operators with Singular Symbols (DOSS) -- Fractional Calculus and Fractional Order Operators -- Boundary Value Problems for Pseudo-Differential Equations with Singular Symbols -- Initial and Boundary Value Problems for Fractional Order Differential Equations -- Distributed and Variable Order Differential-Operator Equations -- Fractional Fokker-Planck-Kolmogorov Equations -- Random Walk Approximants of Mixed and Time-Changed Levy Processes -- Complex DOSS and Systems of Complex Differential Equations -- References 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 HTTP:URL=https://doi.org/10.1007/978-3-319-20771-1

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