In this paper, we investigate the existence, uniqueness and continuous dependence of solutions of fractional neutral functional differential equations with infinite delay and the Caputo fractional derivative order, by means of the Banach's contraction principle and the Schauder's fixed point theorem.

In this article, it is proved that feedback controllers can be designed to stabilize nonlinear neutral stochastic systems with Markovian switching (NSDDEwMS in short) only by using discrete observed state sequences. Due the superlinear coefficients, term and observation data, many routine methods techniques for study of are not applicable. A new Lyapunov functional constructed multiple M-matric...

This paper surveys some results in stochastic differential delay equations beginning with ”On stationary solutions of a stochastic differential equations” by K. Ito and M. Nisio, 1964, and also some results in stochastic stability beginning with the ”Stability of positive supermartingales” by R. Bucy, 1964. The problems discussed in this survey are the existence and uniqueness of solutions of s...