# Introduction to Fractional and Pseudo-Differential Equations with Singular Symbols

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## Description

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.

## ISBN

978-3-319-20770-4

## Publication Date

2015

## Publisher

Springer International Publishing

## City

Cham, Switzerland

## Keywords

Partial Differential Equations, Fractional differential equations, Pseudodifferential operators, Differential equations

## Subject: LCSH

Fractional differential equations, Pseudodifferential operators, Differential equations

## Disciplines

Mathematics

## DOI

10.1007/978-3-319-20771-1

## Repository Citation

Umarov, Sabir, "Introduction to Fractional and Pseudo-Differential Equations with Singular Symbols" (2015). *Mathematics Faculty Book Series*. 4.

https://digitalcommons.newhaven.edu/mathematics-books/4

## Publisher Citation

Sabir Umarov. Introduction to Fractional and Pseudo-Differential Equations with Singular Symbols. Developments in Mathematics, 41. Springer, 2015. ISBN: 978-3-319-20770-4

## Comments

Developments in Mathematics series, no. 41