TY  - JOUR
A1  - Tomovski, Živorad
A1  - Metzler, Ralf
A1  - Gerhold, Stefan
T1  - Fractional characteristic functions, and a fractional calculus approach for moments of random variables
JF  - Fractional calculus and applied analysis : an international journal for theory and applications
N2  - In this paper we introduce a fractional variant of the characteristic function of a random variable. It exists on the whole real line, and is uniformly continuous. We show that fractional moments can be expressed in terms of Riemann-Liouville integrals and derivatives of the fractional characteristic function. The fractional moments are of interest in particular for distributions whose integer moments do not exist. Some illustrative examples for particular distributions are also presented.
KW  - Fractional calculus (primary)
KW  - Characteristic function
KW  - Mittag-Leffler
KW  - function
KW  - Fractional moments
KW  - Mellin transform
Y1  - 2022
U6  - https://doi.org/10.1007/s13540-022-00047-x
SN  - 1314-2224
VL  - 25
IS  - 4
SP  - 1307
EP  - 1323
PB  - De Gruyter
CY  - Berlin ; Boston
ER  - 
TY  - JOUR
A1  - Hedayat Mahmoudi, Mahdi
A1  - Schulze, Bert-Wolfgang
T1  - A new approach to the second order edge calculus
JF  - Journal of pseudo-differential operators and applications
N2  - We establish essential steps of an iterative approach to operator algebras, ellipticity and Fredholm property on stratified spaces with singularities of second order. We cover, in particular, corner-degenerate differential operators. Our constructions are focused on the case where no additional conditions of trace and potential type are posed, but this case works well and will be considered in a forthcoming paper as a conclusion of the present calculus.
KW  - Operators on singular manifolds
KW  - Mellin transform
KW  - Stratified spaces
KW  - Ellipticity and parametrices
Y1  - 2018
U6  - https://doi.org/10.1007/s11868-017-0191-2
SN  - 1662-9981
SN  - 1662-999X
VL  - 9
IS  - 2
SP  - 265
EP  - 300
PB  - Springer
CY  - Basel
ER  -