72 citations · 345 across the 28 of their papers we have counts for
30 papers · 1 filter
Fractional powers of Bessel operator and its numerical calculation
Durdimurod Durdiev, Elina Shishkina, Sergei Sitnik
The article discusses the fractional powers of the Bessel operator and their numerical implementation. An extensive literature is devoted to the study of fractional powers of the L…
On two classes of generalized fractional operators (with short historical survey of fractional calculus)
E. L. Shishkina, S. M. Sitnik
This is a survey paper in two parts. In the first part we list main variants of one-dimensional fractional integrodifferential operators. Also some historical and priority remarks…
On the correctness of finite-rank approximations by series of shifted Gaussians
S. M. Sitnik, A. S. Timashov, S. N. Ushakov
In this paper we consider interpolation problem connected with series by integer shifts of Gaussians. Known approaches for these problems met numerical difficulties. Due to it anot…
The Transmutation Method and Boundary-Value Problems for Singular Differential Equations
V. V. Katrakhov, S. M. Sitnik
The main content of this book is composed from two doctoral theses: by V.\,V.~Katrakhov (1989) and by S.\,M.~Sitnik (2016). In our work, for the first time in the format of a monog…
Monotonicity Properties and functional inequalities for the Volterra and incomplete Volterra functions
Khaled Mehrez, Sergei M. Sitnik
In this paper we prove some monotonicity, log--convexity and log--concavity properties for the Volterra and incomplete Volterra functions. Moreover, as consequences of these result…
Generalized Volterra functions, its integral representations and applications to the Mathieu--type series
Khaled Mehrez, Sergei M. Sitnik
In this paper we introduce the new class of generalized Volterra functions. We prove some integral representations for them via Fox-Wright H-functions and Meijer G-functions. From…