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In this paper, we consider the stochastic evolution of two particles with electrostatic repulsion and restoring force which is modeled by a system of stochastic differential equations driven by fractional Brownian motion where the diffusion coefficients are constant. This is the simplest case for some classes of non- colliding particle systems such as Dyson Brownian motions, Brownian particles systems with nearest neighbour repulsion. We will prove that the equation has a unique non- colliding solution in path- wise sense. | Existence and uniqueness of solutions for twodimensional fractional non- colliding particle systems
