Introduction to Fractional and Pseudo-Differential Equations with Singular Symbols
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Publisher's description: 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.
Contents: 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.
Springer International Publishing
Partial Differential Equations, Fractional differential equations, Pseudodifferential operators, Differential equations
Fractional differential equations, Pseudodifferential operators, Differential equations
Umarov, Sabir, "Introduction to Fractional and Pseudo-Differential Equations with Singular Symbols" (2015). Mathematics Faculty Book Series. 4.
Sabir Umarov. Introduction to Fractional and Pseudo-Differential Equations with Singular Symbols. Developments in Mathematics, 41. Springer, 2015. ISBN: 978-3-319-20770-4