Ulam type stability for first-order linear and nonlinear impulsive fuzzy differential equations

Abstract

This paper gives a number of Ulam type stability results of first-order linear and first-order nonlinear impulsive fuzzy differential equations in different cases by applying an appropriate inequality and the direct analysis method. First, the Ulam type stability results of linear impulsive fuzzy differentiable equations under a<0, (c1)-differentiable are given. Second, the Ulam type stability results of first-order nonlinear impulsive fuzzy differentiable equations under a<0, (c1)-differentiable and a<0, (c2)-differentiable are presented. Finally, examples are provided to illustrate our results. Our results transfer the corresponding results for impulsive ordinary differential equations to impulsive fuzzy ordinary differential equations.