In this paper we are concerned with a nonlocal problem of a stochastic differential equation that contains a Brownian motion. The solution contains both of mean square Riemann and mean square Riemann-Steltjes integrals, so we study an existence theorem for unique mean square continuous solution and its continuous dependence of the random data X 0 and the (non-random data) coefficients of the nonlocal condition ak. Also, a stochastic differential equation with the integral condition will be considered.

Abstract. In this paper we are concerned with a nonlocal problem of a coupled system of differential equations. We study the local existence of the solution and its continuous dependence. The global existence and its uniform stability is being studied.Mathematics subject classification (2010): 34B18, 34B10.

Abstract. In this paper we are concerned with an initial value problem of random fractional-order differential equation with nonlocal condition. Continuous dependence and some other properties concerning the existence and uniqueness of the solution will be proved.Mathematics subject classification (2010): 26A33, 34K50.

In this paper we are concerned with Itô problem of stochastic differential equation with nonlocal condition, the solution is represented as a stochastic integral equation that contains Itô integral. We study the existence of at least mean square continuous solution for this type. The existence of the maximal and minimal solutions will be proved.

In this paper we are concerned with a nonlocal problem of a stochastic differential equation that contains a Brownian motion. The solution contains both of mean square Riemann and mean square Riemann-Steltjes integrals, so we study an existence theorem for unique mean square continuous solution and its continuous dependence of the random data X 0 and the (non-random data) coefficients of the