A unified convergence analysis for a certain family of iterative algorithms with applications to fractional calculus

We present local and semilocal convergence results for some iterative algorithms in order to approximate a locally unique solution of a nonlinear equation in a Banach space setting. In earlier studies to operator involved is assumed to be at least once Fréchetdifferentiable. In the present study, we assume that the operator is only continuous. This way we expand the applicability of these iterative algorithms. In the third part of the study we present some choices of the operators involved in fractional calculus where the operators satisfy the convergence conditions