Advances in the Qualitative Theory of Integro-Differential Equations

Abstract

This work investigates the advances from the past until now in the qualitative properties of solutions of linear and nonlinear integro-differential equations (IDEs). Here, we present an extensive literature on the qualitative properties of solutions, including asymptotic stability, uniform stability, instability and global uniform asymptotic stability of the zero solution, as well as boundedness, square integrability and existence of solutions to various linear and non-linear Volterra IDEs, without delay and with delay. We also present some applications of such equations in sciences and engineering. Some examples are given to illustrate the results of this work and show their applications. © 2023 Nova Science Publishers, Inc. All rights reserved.