A novel fixed point iteration process applied in solving the Caputo type fractional differential equations in Banach spaces

Abstract

We introduce the modified Picard-Ishikawa hybrid iterative scheme and establish some strong convergence results for the class of asymptotically generalized phi-pseudocontractive mappings in the intermediate sense in Banach spaces and approximate the fixed point of this class of mappings via the newly introduced iteration scheme. We construct some numerical examples to support our results. Furthermore, we apply the Picard-Ishikawa hybrid iteration scheme in solving the nonlinear Caputo type fractional differential equations. Our results generalize, extend and unify several existing results in literature.