ON THE CONVERGENCE OF ITERATIVE METHODS WITH APPLICATIONS IN GENERALIZED FRACTIONAL CALCULUS

Abstract

We present a semilocal convergence study of some iterative methods on a generalized Banach space setting to approximate a locally unique zero of an operator. Earlier studies such as [7, 8, 9, 14] require that the operator involved is Frechet-differentiable. In the present study we assume that the operator is only continuous. This way we extend the applicability of these methods to include generalized fractional calculus and problems from other areas. Some applications include generalized fractional calculus involving the Riemann- Liouville fractional integral and the Caputo fractional derivative. Fractional calculus is very important for its applications in many applied sciences.