-This paper deals with the adapted Milstein method for solving linear stochastic delay differential equations. It is proved that the numerical method is mean-square (MS) stable under suitable conditions. The obtained result shows that the method preserves the stability property of a class of linear constant-coefficient problems. This is also verified by several numerical examples. (~) 2006 Else...

This paper is devoted to the study of stochastic fractional differential equations. Particularly, we existence and uniqueness solutions nonlinear weighted impulsive ψ -Hilfer neutral integro-fractional system with infinite delay. We obtain results help fixed-point theorems Banach contraction principle. Additionally, inve...

By means of the averaging technique and the generalized Riccati transformation technique, we establish some oscillation criteria for the second-order quasilinear neutral delay dynamic equations r t |xΔ t |γ−1xΔ t Δ q1 t |y δ1 t |α−1y δ1 t q2 t |y δ2 t |β−1y δ2 t 0, t ∈ t0,∞ T, where x t y t p t y τ t , and the time scale interval is t0,∞ T : t0,∞ ∩ T. Our results in this paper not only extend t...