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  - Tomovski, Zivorad
A1  - Sandev, Trifce
A1  - Metzler, Ralf
A1  - Dubbeldam, Johan
T1  - Generalized space-time fractional diffusion equation with composite fractional time derivative
JF  - Physica : europhysics journal ; A, Statistical mechanics and its applications
N2  - We investigate the solution of space-time fractional diffusion equations with a generalized Riemann-Liouville time fractional derivative and Riesz-Feller space fractional derivative. The Laplace and Fourier transform methods are applied to solve the proposed fractional diffusion equation. The results are represented by using the Mittag-Leffler functions and the Fox H-function. Special cases of the initial and boundary conditions are considered. Numerical scheme and Grunwald-Letnikov approximation are also used to solve the space-time fractional diffusion equation. The fractional moments of the fundamental solution of the considered space-time fractional diffusion equation are obtained. Many known results are special cases of those obtained in this paper. We investigate also the solution of a space-time fractional diffusion equations with a singular term of the form delta(x). t-beta/Gamma(1-beta) (beta > 0).
KW  - Fractional diffusion equation
KW  - Composite fractional derivative
KW  - Riesz-Feller fractional derivative
KW  - Mittag-Leffler functions
KW  - Fox H-function
KW  - Fractional moments
KW  - Asymptotic expansions
KW  - Grunwald-Letnikov approximation
Y1  - 2012
U6  - https://doi.org/10.1016/j.physa.2011.12.035
SN  - 0378-4371
SN  - 1873-2119
VL  - 391
IS  - 8
SP  - 2527
EP  - 2542
PB  - Elsevier
CY  - Amsterdam
ER  -