In this short note we present a new general definition of local fractional derivative, that depends on an unknown kernel. For some appropriate choices of the kernel we obtain some known cases. We establish a relation between this new concept and ordinary differentiation. Using such formula, most of the fundamental properties of the fractional derivative can be derived directly.
@article{bwmeta1.element.doi-10_1515_math-2016-0104,
author = {Ricardo Almeida and Ma\l gorzata Guzowska and Tatiana Odzijewicz},
title = {A remark on local fractional calculus and ordinary derivatives},
journal = {Open Mathematics},
volume = {14},
year = {2016},
pages = {1122-1124},
zbl = {1355.26005},
language = {en},
url = {http://dml.mathdoc.fr/item/bwmeta1.element.doi-10_1515_math-2016-0104}
}
Ricardo Almeida; Małgorzata Guzowska; Tatiana Odzijewicz. A remark on local fractional calculus and ordinary derivatives. Open Mathematics, Tome 14 (2016) pp. 1122-1124. http://gdmltest.u-ga.fr/item/bwmeta1.element.doi-10_1515_math-2016-0104/