Convergence and Data Dependence for Fractional Integro-Differential Equations with Picard’s Three-Step Iteration Algorithm

Abstract

Fractional calculus, which involves derivatives and integrals of non-integer order, is widely used in modeling real-world problems in science and engineering. This study focuses on solving fractional integro-differential equations using Picard's three-step iteration algorithm. We apply the Picard's three-step iteration algorithm to approximate solutions and show that it converges strongly. We also investigate the data dependence of the solution. Therefore, we present new results for approximating the solution of the Riemann-Liouville fractional integro-differential equation and for data dependence.