A FIXED POINT APPROACH TO FRACTIONAL INTEGRO-DIFFERENTIAL EQUATIONS: CONVERGENCE AND DATA DEPENDENCE

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 Picard's three-step iteration algorithm to approximate solutions and show that it converges strongly. The method is shown to be not only efficient in approximating solutions but also robust with respect to perturbations in the initial data and operators, demonstrating its data dependence. A numerical example is provided to illustrate the theoretical results and to confirm the applicability and reliability of the proposed approach.