EXISTENCE AND STABILITY RESULTS FOR STOCHASTIC FRACTIONAL NEUTRAL DIFFERENTIAL EQUATIONS WITH GAUSSIAN NOISE AND LÉVY NOISE

Abstract

In this paper we prove the existence and uniqueness of solution of stochastic fractional neutral differential equations with Gaussian noise or Lévy noises by using the Picar-Lindelöf successive approximation scheme. Further stability results of nonlinear stochastic fractional dynamical system with Gaussian and Lévy noises are established. Examples are provided to illustrate the theoretical results.