Introduction to Fractional and Pseudo-Differential Equations with Singular Symbols

  • Sabir Umarov

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

Authors and affiliations

  • Sabir Umarov
    • 1
  1. 1.Department of MathematicsUniversity of New HavenWest HavenUSA

Bibliographic information

  • DOI https://doi.org/10.1007/978-3-319-20771-1
  • Copyright Information Springer International Publishing Switzerland 2015
  • Publisher Name Springer, Cham
  • eBook Packages Mathematics and Statistics
  • Print ISBN 978-3-319-20770-4
  • Online ISBN 978-3-319-20771-1
  • Series Print ISSN 1389-2177
  • Series Online ISSN 2197-795X
  • About this book