On q–Analogues of Caputo Derivative and Mittag–Leffler Function
Fractional calculus and applied analysis, Tome 10 (2007) no. 4, pp. 359-373
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
@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
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/