Different stabilities for integrodifferential evolution equations with nonlocal conditions and application to epidemiology

Abstract

Integrodifferential evolution equations are becoming increasingly popular in many fields because of their ability to model and assess complicated procedures. In this paper, we study different kinds of stabilities for integrodifferential evolution equations with nonlocal conditions. The concept of σ–semi–Hyers–Ulam stability, which lies somewhere between the Hyers–Ulam and Hyers–Ulam–Rassias stabilities, will be specifically discussed. In order to ensure Hyers–Ulam– Rassias, σ–semi–Hyers–Ulam, and Hyers–Ulam stabilities for integro– differential evolution equations with nonlocal conditions, this is taken into consideration within a framework of suitable metric spaces. We will examine the many situations in which the integrals are defined on both finite and infinite intervals. Fixed–point arguments and generalizations of the Bielecki metric are two of the techniques employed. To illustrate the main results, we also provide examples. The epidemiology application for modeling the transmission of infectious diseases served as a source of interest.