Stability analysis of damped fractional stochastic differential systems with Poisson jumps: an successive approximation approach

This paper aims to investigate a new class of fractional stochastic differential systems under the influence of damping and Poisson jumps. First, the existence and uniqueness of mild solutions for the proposed system are investigated under the non-Lipschitz conditions. The results are formulated and proved by using the (β,δ)-regularised family, Grönwall's inequality, and successive approximation technique, which is different from the fixed point approach. Moreover, novel stability criteria for the considered system are obtained by utilising the corollary of the Bihari inequality. Finally, the correctness of the obtained results is verified by example.