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 Vestnik SamU. Estestvenno-Nauchnaya Ser., 2017, Issue 2, Pages 32–43 (Mi vsgu540)

Mathematics

On some qualitative properties of the operator of fractional differentiation in Kipriyanov sense

M. V. Kukushkin

Institute of Applied Mathematics and Automatization, 89a, Shortanova street, Nalchik, 360000, Russian Federation

Abstract: In this paper we investigated the qualitative properties of the operator of fractional differentiation in Kipriyanov sense. Based on the concept of multidimensional generalization of operator of fractional differentiation in Marchaud sense we have adapted earlier known techniques of proof theorems of one-dimensional theory of fractional calculus for the operator of fractional differentiation in Kipriyanov sense. Along with the previously known definition of the fractional derivative in the direction we used a new definition of multidimensional fractional integral in the direction of allowing you to expand the domain of definition of formally adjoint operator. A number of theorems that have analogs in one-dimensional theory of fractional calculus is proved. In particular the sufficient conditions of representability of a fractional integral in the direction are received. Integral equality the result of which is the construction of the formal adjoint operator defined on the set of functions representable by the fractional integral in direction is proved.

Keywords: fractional differentiation, operator of Marchaud, operator of Riemann–Liouville, fractional derivative in the direction, fractional integral, energetic space, formally conjugated operator, accretive operator.

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Citation: M. V. Kukushkin, “On some qualitative properties of the operator of fractional differentiation in Kipriyanov sense”, Vestnik SamU. Estestvenno-Nauchnaya Ser., 2017, no. 2, 32–43

Citation in format AMSBIB
\Bibitem{Kuk17} \by M.~V.~Kukushkin \paper On some qualitative properties of the operator of fractional differentiation in Kipriyanov sense \jour Vestnik SamU. Estestvenno-Nauchnaya Ser. \yr 2017 \issue 2 \pages 32--43 \mathnet{http://mi.mathnet.ru/vsgu540} \elib{https://elibrary.ru/item.asp?id=29957949} 

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This publication is cited in the following articles:
1. M. U. Yakhshiboev, “O drobnom integrodifferentsirovanii Adamara i tipa Adamara po napravleniyu v vesovykh prostranstvakh Lebega so smeshannoi normoi”, Vladikavk. matem. zhurn., 22:4 (2020), 119–134
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