Generalized Fractional Differential Equations

  • Vassili Kolokoltsov
Part of the Birkhäuser Advanced Texts Basler Lehrbücher book series (BAT)


In this chapter, the theory of linear and nonlinear fractional differential equations is developed and extended to a large class of generalized fractional evolutions. The used method is mostly that of semigroups and propagators as developed in Chapters 4 and 5. As previously, general facts are illustrated on concrete examples. The generalized fractional calculus is usually developed by extending fractional integrals to integral operators with arbitrary integral kernels (or some of their subclasses dictated by the classes of special functions under investigation) and then defining fractional derivatives as the derivatives of these integral operators.


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© Springer Nature Switzerland AG 2019

Authors and Affiliations

  • Vassili Kolokoltsov
    • 1
    • 2
  1. 1.Department of StatisticsUniversity of WarwickWarwickUK
  2. 2.Higher School of EconomicsMoscowRussia

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