Iterative methods and their applications to Banach space valued functions in abstract fractional calculus


Explicit iterative methods have been used extensively to generate a sequence approximating a solution of an equation on a Banach space setting. However, little attention has been given to the study of implicit iterative methods. We show a semi-local convergence analysis for a some general implicit and explicit iterative techniques. Illustrative applications are presented including Banach space valued functions of fractional calculus, such that all integrals are of Bochner-type.

Publication Title

Progress in Fractional Differentiation and Applications