Stability analysis and data sensitivity of fractional integro-differential equations

Abstract

The paper focuses on analyzing the Ulam stability and data dependence in fractional integro-differential equations with Caputo-type fractional derivatives. The main aim of the work is to see under which circumstances the solutions remain stably behaved with respect to small perturbations in the initial data and the parameters of the system. Using a nonlinear integral inequality of the Henry-Gronwall kind, four types of stabilities are studied and discussed. From there, several examples are shown that illustrate the theory. Also, there are some graphs to show how the system solutions behave and to depict the sensitive nature of the system concerning input data changes. The results provide valuable insights into the stability aspects of fractional dynamic systems and support existing research in fractional calculus and their applications.