No abstract

This paper mainly discusses the existence and finite-time stability of solutions for impulsive fractional stochastic differential equations (IFSDEs). By applying the Picard-Lindelöf iteration method of successive approximation scheme, we establish the existence results of solutions. Subsequently, the uniqueness of solution is derived by the method of contradiction. In addition, we investigate the finite-time stability by means of the generalized Grönwall-Bellman inequality. As an application, examples are provided to expound our theoretical conclusions.

This article studies a new kind of Ψ -Hilfer fractional system driven by m -dimensional Brownian motion. By utilizing the generalized Laplace transform and its inverse, the contraction mapping principle, and the properties of a semigroup, we establish the uniqueness of the solution. In addition, finite-time stability is investigated by means of the properties of norm and inequalities scaling technique. As verification, an example is given to show the deduced conclusions.

No abstract