*Article* **On a Coupled System of Random and Stochastic Nonlinear Differential Equations with Coupled Nonlocal Random and Stochastic Nonlinear Integral Conditions**

**Ahmed M. A. El-Sayed \* and Hoda A. Fouad \***

**\*** Correspondence: amasayed@alexu.edu.eg (A.M.A.E.-S.); hoda.fouad@alexu.edu.eg (H.A.F.)

**Abstract:** It is well known that Stochastic equations had many useful applications in describing numerous events and problems of real world, and the nonlocal integral condition is important in physics, finance and engineering. Here we are concerned with two problems of a coupled system of random and stochastic nonlinear differential equations with two coupled systems of nonlinear nonlocal random and stochastic integral conditions. The existence of solutions will be studied. The sufficient condition for the uniqueness of the solution will be given. The continuous dependence of the unique solution on the nonlocal conditions will be proved.

**Keywords:** stochastic processes; stochastic differential equation; coupled system; nonlocal stochastic integral conditions

**MSC:** 34A12; 34A30; 34D20; 34F05; 60H10
