Existence, uniqueness and continuous dependence of solutions to conformable stochastic differential equations

In this paper, we study conformable stochastic differential equations. Firstly, the Itô formula is established and used to discuss the explicit expression of solutions of linear differential equations. Secondly, the existence and uniqueness of solutions of nonlinear conformable stochastic differential equations are proved by the Picard iteration method, and the continuous dependence of solutions on initial values is proved by the Gronwall inequality, the exponential estimation of solutions is also given. Finally, some examples are given to illustrate the theoretically results and we compare the simulation results for the conformable stock model with different ρ.