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© 2015

Introduction to Fractional and Pseudo-Differential Equations with Singular Symbols

  • A novel theory of pseudo-differential operators and equations with symbols singular in dual variables is presented systematically

  • Recent developments in the theory of fractional order differential equations and their various applications are studied

  • Fractional Fokker-Planck-Kolmogorov equations and their connection with the associated stochastic differential equations driven by a time-changed process are discussed in detail

Book

Part of the Developments in Mathematics book series (DEVM, volume 41)

About this book

Introduction

​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.

Keywords

Complex Fourier Transform Fokker-Planck-Kolmogorov Equations Fractional Differential Equations Levy Processes Pseudo-Differential Equations partial differential equations

Authors and affiliations

  1. 1.Department of MathematicsUniversity of New HavenWest HavenUSA

Bibliographic information

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Reviews

“The book systematically presents the theory of pseudo-differential operators with symbols singular in dual variables. … The book is interesting both for probabilists and for researchers in those areas of functional analysis where pseudo-differential operators arise. The interesting connections are emphasized by a multitude of examples. Additional notes at the end of each chapter provide nice historical insights and help to understand the role of the presented results within the big picture.” (Alexander Schnurr, zbMATH 1331.35005, 2016)