On a Neutral It<i>ô</i> and Arbitrary (Fractional) Orders Stochastic Differential Equation with Nonlocal Condition

Abstract

In this paper, we are concerned with the combinations of the stochastic Itô-differential and the arbitrary (fractional) orders derivatives in a neutral differential equation with a stochastic, nonlinear, nonlocal integral condition. The existence of solutions will be proved. The sufficient conditions for the uniqueness of the solution will be given. The continuous dependence of the unique solution will be studied.

Keywords

• stochastic processes
• stochastic differential equation
• It<i>ô</i>-differential
• fractional differential equations
• coupled system
• nonlocal stochastic integral conditions