Ulam type stability analysis of solutions to nonlinear fractional differential equations with integral boundary conditions

Abstract

This manuscript investigates four types of Ulam stability: Hyers–Ulamstability, generalized Hyers–Ulam stability, Hyers–Ulam–Rassias stability, andgeneralized Hyers–Ulam–Rassias stability of solutions to a specific class ofhigh–order nonlinear fractional differential equations involving the Riemann–Liouville fractional derivative. The problem is considered under integralboundary conditions that incorporate both the initial and terminal points ofthe domain. The analysis primarily relies on the application of the Gronwalllemma. To validate the theoretical results, several illustrative examples arepresented. Additionally, graphical simulations are performed to further sup-port the analytical findings, highlighting the effectiveness of the proposedapproach within the framework of fractional calculus. This work extendsand improves upon existing results in the literature by generalizing from lin-ear to nonlinear cases. The findings contribute significantly to the study of fractional differential equations and provide valuable insights for applica-tions in physics, engineering, and control theory.