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

Syed Omar Shah (), Sanket Tikare and Mawia Osman
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Syed Omar Shah: School of Mathematical Sciences, Zhejiang Normal University, Jinhua 321004, China
Sanket Tikare: Department of Mathematics, Ramniranjan Jhunjhunwala College, Mumbai 400 086, Maharashtra, India
Mawia Osman: School of Mathematical Sciences, Zhejiang Normal University, Jinhua 321004, China

Mathematics, 2023, vol. 11, issue 21, 1-12

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; impulses (search for similar items in EconPapers)
JEL-codes: C (search for similar items in EconPapers)
Date: 2023
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