Quantum mechanics

Differential equation

Exponential stability

Applied mathematics

Stability (learning theory)

Computer science

Dentistry

Thermodynamics

Physics

Nonlinear system

Calculus (dental)

Scalar (mathematics)

Volterra integral equation

Mathematics

Differential (mechanical device)

Lyapunov function

Mathematical analysis

Geometry

Medicine

Volterra equations

Integral equation

Machine learning

Arab Journal of Basic and Applied Sciences

In this paper, we consider certain non-linear scalar Volterra integro-differential equations and Volterra integro-differential systems of first order. We investigate the boundedness, stability, uniformly asymptotic stability, integrability and square integrability of solutions to the scalar equations and the system considered. The technique used to prove the results of the paper is based on the second method of Lyapunov. From the obtained results, we extend and improve some related results that can be found in the literature.

New qualitative criteria for solutions of Volterra integro-differential equations