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Gel’fond-Leont’ev Integration Operators of Fractional (Multi-)Order Generated by Some Special Functions.
- Source :
-
AIP Conference Proceedings . 2018, Vol. 2048 Issue 1, p050016-1-050016-10. 10p. - Publication Year :
- 2018
-
Abstract
- In this paper we survey some author’s results and developments relating the so-called Gel’fond-Leont’ev (G-L) operators of generalized integration and differentiation, classes of special functions (SF) of generalized hypergeometric type and the operators of generalized fractional calculus (GFC). The G-L operators have been introduced by Gel’fond-Leont’ev [9] in the classes of analytic functions in disks ΔR = {|z| < R}, by means of of multipliers’ sequences composed by the coefficients of suitable entire (generating) functions. Introducing classes of SF related to Fractional Calculus (FC), as the Mittag-Leffler (ML) function, the multi-index Mittag-Leffler (multi-ML) function and its various particular cases ([16]–[18]), we specify the G-L operators generated by these entire functions. It is shown that in these cases, the G-L operators can be extended to analytic functions in wider complex domains Ω starlike with respect to the origin z = 0 and represented by operators of the Generalized Fractional Calculus (GFC), Kiryakova [14], i.e. operators of generalized integration and differentiation of arbitrary fractional multi-order. Illustrative examples and some open problems are proposed. [ABSTRACT FROM AUTHOR]
Details
- Language :
- English
- ISSN :
- 0094243X
- Volume :
- 2048
- Issue :
- 1
- Database :
- Academic Search Index
- Journal :
- AIP Conference Proceedings
- Publication Type :
- Conference
- Accession number :
- 133543888
- Full Text :
- https://doi.org/10.1063/1.5082115