Well posedness of second-order non-instantaneous impulsive fractional neutral stochastic differential equations

In this manuscript, the authors established existence, uniqueness and stability results for the second-order non -instantaneous impulsive fractional neutral stochastic differential equations (NIIFNSDEs). At first, existence and uniqueness results are obtained by using Caputo fractional derivative (fractional calculus), stochastic technique and fixed point approach with appropriate hypotheses on non-linear continuous functions. Secondly, we discuss the Ulam-Hyers Rassias stability and henceforth, we study Ulam-Hyers stability for NIIFNSDEs. Finally, an example is provided to validate the theoretical findings.(c) 2023 Elsevier Masson SAS. All rights reserved.