An Analysis of the Hyers‐Ulam Stability and Existence of the Nonlinear Multi‐Term Equation for S‐Hilfer Fractional Integrodifferential Equation

ABSTRACT In this paper, Hyers‐Ulam stability is demonstrated for nonlinear multi‐term equations for ‐Hilfer fractional integrodifferential equation with Riemann‐Liouville type boundary conditions involving nonintersecting finite many strips of arbitrary length. Some specified assumptions are supposed to be satisfied by the nonlinear item. In addition to Banach's contraction mapping principle, the Krasnosel'skii fixed‐point theorem and the Leray‐Schauder nonlinear alternative are used to establish the uniqueness result. In addition, as auxiliary results, this paper presents new inequalities for fractional differential equations that can be used to examine Hyers‐Ulam stability based on techniques from nonlinear functional analysis. To illustrate the application of the main results, an example is provided. The analysis reveals that the condition behaves differently depending on whether the orders in the equation are significantly different or close in value.