Recently Kiryakova and several other ones have investigated so-called
multiindex Mittag-Leffler functions associated with fractional calculus.
Here, in this paper, we aim at establishing a new fractional integration
formula (of pathway type) involving the generalized multiindex Mittag-Leffler
function E?,k[(?j,?j)m;z]. Some interesting special cases of our main result
are also considered and shown to be connected with certain known ones.
AbstractIn 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.
A remark on local fractional calculus and ordinary derivatives