Existence, Uniqueness and Successive Approximations for Implicit Caputo Tempered Fractional Differential Equations

Abstract

This study aims to analyze the global convergence and uniqueness properties of the successive approximations method when applied to Caputo tempered fractional differential equations. We provide rigorous mathematical proofs to establish the convergence of the method, ensuring that the iterative process converges to a unique solution. Furthermore, we investigate the impact of the nonlocal conditions on the uniqueness of the solution obtained through the successive approximations method.