Boundedness and asymptotic stability of nonlinear Volterra integro-differential equations using Lyapunov functional

In this paper, I consider Lyapunov functionals combined with the Laplace transform to obtain boundedness results regarding the solutions of the nonlinear Volterra integro-differential equations x'(t) = A(t)x(t) + B(t) + integral(t)(0) C(t, s)f (x(s))ds + g(x(t)). Asymptotic stability results regarding the zero solution are carried out for the case where B(t)is identically zero. Numerical examples are proposed to perform the given results. (C) 2018 The Author. Production and hosting by Elsevier B.V. on behalf of King Saud University.