Stefan Samko

TL;DR: Fractional integrals and derivatives on an interval fractional integral integrals on the real axis and half-axis further properties of fractional integral and derivatives, and derivatives of functions of many variables applications to integral equations of the first kind with power and power-logarithmic kernels integral equations with special function kernels applications to differential equations as discussed by the authors.

TL;DR: In this paper, the interpretation and differentiation of functions to a variable order (d/dx)nf(x) is studied in two ways: 1) using the Riemann-Liouville definition, 2) using Fourier transforms Some properties and the inversion formula are obtained

TL;DR: In this article, the authors survey some properties of completely monotonic functions and give various examples, including some famous special functions such as the Laplace transform of an infinitely divisible probability distribution on (0, ∞).

TL;DR: The authors presented a broadened version of the plenary lecture presented by the author at the conference Analytic Methods of Analysis and Differential Equations (AMADE-2003), September 4-9, 2003.

TL;DR: The Reisz potential operator and the Lizorkin type invarient spaces have been used in the theory of special functions and operator theory as discussed by the authors, as well as in functional spaces on the unit sphere.