Ulam Type Stability Results of Nonlinear Impulsive Volterra–Fredholm Integro-Dynamic Adjoint Equations on Time Scale

Abstract

This paper is dedicated to exploring the existence, uniqueness and Ulam stability analysis applied to a specific class of mathematical equations known as nonlinear impulsive Volterra Fredholm integro-dynamic adjoint equations within finite time scale intervals. The primary aim is to establish sufficient conditions that demonstrate Ulam stability for this particular class of equations on the considered time scales. The research methodology relies on the Banach contraction principle, Picard operator and extended integral inequality applicable to piecewise continuous functions on time scales. To illustrate the applicability of the findings, an example is provided.

Keywords

• Volterra integral
• existence
• uniqueness
• time scale
• Hyers–Ulam stability
• Hyers–Ulam–Rassias stability