AbstractThe goal of this paper is to present a semi-local convergence analysis for some iterative methods under generalized conditions. The operator is only assumed to be continuous and its domain is open. Applications are suggested including Banach space valued functions of fractional calculus, where all integrals are of Bochner-type.
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.
Iterative Convergence with Banach Space Valued Functions in Abstract Fractional Calculus
