On q–Analogues of Caputo Derivative and Mittag–Leffler Function
Fractional calculus and applied analysis, Tome 10 (2007) no. 4, pp. 359-373
Voir la notice de l'article provenant de la source Bulgarian Digital Mathematics Library
Based on the fractional q–integral with the parametric lower limit of
integration, we consider the fractional q–derivative of Caputo type.
Especially, its applications to q-exponential functions allow us to introduce
q–analogues of the Mittag–Leffler function. Vice versa, those functions can
be used for defining generalized operators in fractional q–calculus.
Keywords:
Mittag-Leffler Function, q–Integral, q–Derivative, Fractional Integral, Fractional Derivative, 33D60, 33E12, 26A33
Rajkovic, Predrag; Marinkovic, Sladjana; Stankovic, Miomir. On q–Analogues of Caputo Derivative and Mittag–Leffler Function. Fractional calculus and applied analysis, Tome 10 (2007) no. 4, pp. 359-373. http://geodesic.mathdoc.fr/item/FCAA_2007_10_4_a1/
@article{FCAA_2007_10_4_a1,
author = {Rajkovic, Predrag and Marinkovic, Sladjana and Stankovic, Miomir},
title = {On {q{\textendash}Analogues} of {Caputo} {Derivative} and {Mittag{\textendash}Leffler} {Function}},
journal = {Fractional calculus and applied analysis},
pages = {359--373},
year = {2007},
volume = {10},
number = {4},
language = {en},
url = {http://geodesic.mathdoc.fr/item/FCAA_2007_10_4_a1/}
}
TY - JOUR AU - Rajkovic, Predrag AU - Marinkovic, Sladjana AU - Stankovic, Miomir TI - On q–Analogues of Caputo Derivative and Mittag–Leffler Function JO - Fractional calculus and applied analysis PY - 2007 SP - 359 EP - 373 VL - 10 IS - 4 UR - http://geodesic.mathdoc.fr/item/FCAA_2007_10_4_a1/ LA - en ID - FCAA_2007_10_4_a1 ER -
%0 Journal Article %A Rajkovic, Predrag %A Marinkovic, Sladjana %A Stankovic, Miomir %T On q–Analogues of Caputo Derivative and Mittag–Leffler Function %J Fractional calculus and applied analysis %D 2007 %P 359-373 %V 10 %N 4 %U http://geodesic.mathdoc.fr/item/FCAA_2007_10_4_a1/ %G en %F FCAA_2007_10_4_a1