This work studies certain perturbed and un-perturbed nonlinear systems of continuous discrete integro-delay differential equations (IDDEs). Using the Lyapunov–Krasovskii functional (LKF) method Lyapunov–Razumikhin (LRM), uniform asymptotic stability (UAS), (US), integrability boundedness solutions as well exponential (ES) instability are discussed. In this paper, five new theorems a corollary g...

In this paper, by the weighted ergodic function based on the measure theory, we study the pseudo asymptotic behavior of mild solution for semilinear fractional integro-differential equations. The existence, unique of -pseudo anti-periodic ( -pseudo periodic, -pseudo almost periodic, -pseudo almost automorphic) solution are investigated. Moreover, an application to fractional partial differentia...

Abstract: In this paper we shall investigate the asymptotic behavior (at +∞) of certain classes of functional differential equations, involving causal (abstract Volterra) operators. Vast literature exists on this subject, mainly in the case of ordinary differential equations, delay equations and integro-differential equations. We mention here the book, non-linear differential equations, by G. S...

We review our algebraic framework for linear boundary problems (concentrating on ordinary differential equations). Its starting point is an appropriate algebraization of the domain of functions, which we have named integro-differential algebras. The algebraic treatment of boundary problems brings up two new algebraic structures whose symbolic representation and computational realization is base...

To solve the weakly-singular Volterra integro-differential equations, the combined method of the Laplace Transform Method and the Adomian Decomposition Method is used. As a result, series solutions of the equations are constructed. In order to explore the rapid decay of the equations, the pade approximation is used. The results present validity and great potential of the method as a powerful al...

This paper is related to the existence and approximation of solutions for impulsive functional differential equations with periodic boundary conditions. We study the existence and approximation of extremal solutions to different types of functional differential equations with impulses at fixed times, by the use of the monotone method. Some of the options included in this formulation are differe...

Some New Uniqueness Results of Solutions for Fractional Volterra-Fredholm Integro-Differential Equations