Hyers-Ulam-Rassias Stability of Certain Classes of Nonlinear Functional Differential Equations of Third Order

Abstract

This paper investigates the Hyers-Ulam-Rassias stability of specific classes of third-order nonlinear functional differential equations, building on the foundational concepts introduced by Ulam and Hyers. The primary objective is to derive stability conditions and Hyers-Ulam-Rassias constants for these equations. Using Bihari integral inequality and Gronwall-Bellman-Bihari type inequalities as the methodological framework, the stability results are rigorously established. The findings are illustrated through practical examples, demonstrating the applicability of the derived stability conditions to problems in fields such as hereditary dynamics, population growth models, and the spread of infectious diseases. These results contribute to both the theoretical understanding and practical application of stability analysis in nonlinear differential equations.