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


​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.


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

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