Hyers–Ulam stability of impulsive Volterra delay integro-differential equations

Abstract

Abstract This paper discusses different types of Ulam stability of first-order nonlinear Volterra delay integro-differential equations with impulses. Such types of equations allow the presence of two kinds of memory effects represented by the delay and the kernel of the used fractional integral operator. Our analysis is based on Pachpatte’s inequality and the fixed point approach represented by the Picard operators. Applications are provided to illustrate the stability results obtained in the case of a finite interval.

Keywords

• Ulam–Hyers stability
• Delay integro-differential equation
• Impulses