Stability of a Volterra Integral Equation on Time Scales

2017/01/05 by Alaa E. Hamza, Hamza, Alaa E., Ahmed G. Ghallab +1
Mathematics · #Dynamical Systems (math.DS) #FOS: Mathematics #Functional Equations Stability Results #Mathematical and Theoretical Analysis #Numerical methods for differential equations

paper · pdf · doi:10.48550/arxiv.1701.01217

openalex publication_date 2017/01/05 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

In this paper, we study Hyers-Ulam stability for integral equation of Volterra type in time scale setting. Moreover we study the stability of the considered equation in Hyers-Ulam-Rassias sense. Our technique depends on successive approximation method, and we use time scale variant of induction principle to show that equation (1.1) is stable on unbounded domains in Hyers-Ulam-Rassias sense.

Citations

• On the stability of the linear mapping in Banach spaces

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• On the Ulam Type Stability of Nonlinear Volterra Integral Equations
• Basics of Volterra integral equations on time scales
• Existence Results by The Method of Upper and Lower Solutions for Volterra Integral Equation on Time Scales
• Hyers--Ulam Stability for Discrete Time Scale with Two Step Sizes
• The Hyers-Ulam stability for nonlinear Volterra integral equations via a generalized Diaz-Margolis's fixed point theorem