We consider a new fractional impulsive differential hemivariational inequality, which captures the required characteristics of both the hemivariational inequality and the fractional impulsive differential equation within the same framework. By utilizing a surjectivity theorem and a fixed point theorem we establish an existence and uniqueness theorem for such a problem. Moreover, we investigate the perturbation problem of the fractional impulsive differential hemivariational inequality to prove a convergence result, which describes the stability of the solution in relation to perturbation data. Finally, our main results are applied to obtain some new results for a frictional contact problem with the surface traction driven by the fractional impulsive differential equation.

我们考虑了一种新的分数脉冲微分半变分不等式，它在同一框架内捕获了半变分不等式和分数脉冲微分方程所需的特征。通过利用满射性定理和不动点定理，我们为此类问题建立了存在唯一性定理。此外，我们研究了分数脉冲微分半变分不等式的摄动问题，以证明收敛结果，它描述了与摄动数据相关的解的稳定性。最后，我们的主要结果被应用于获得由分数脉冲微分方程驱动的表面牵引摩擦接触问题的一些新结果。