In this paper stability inequalities for the linear nonhomogeneous Volterra delay integro-differential equation (VDIDE) is being established. The particular problems are encountered to show applicability of method and confirm predicted theoretical analysis.

In this article, the backstepping control scheme is proposed to stabilize fractional order Riccati matrix differential equation with retarded arguments in which derivative presented using Caputo's definition of derivative. The results are established Mittag-Leffler stability. Lyapunov function defined at each stage and negativity an overall ensured by proper selection law. Numerical simulation ...

Dynamic systems in many branches of science and industry are often perturbed by various types of environmental noise. Analysis of this class of models are very popular among researchers. In this paper, we present a method for approximating solution of fractional-order stochastic delay differential equations driven by Brownian motion. The fractional derivatives are considered in the Caputo sense...