The goal of this paper is to introduce and study a new class of fractional differential hemivariational inequality formulated by an evolutionary hemivariational inequality and a fractional differential equation in Banach spaces. By employing the Rothe method and the surjectivity result, we derive the existence of unique solution for such a problem under some mild conditions. Moreover, we use the fully discrete scheme to approximate the fractional differential hemivariational inequality and provide an error estimate for the approximation. Finally, the main results are applied to obtain the unique solvability as well as the numerical analysis for a viscoelastic frictional contact problem with adhesion.

本文的目的是介绍和研究一类新的分数阶微分半变分不等式，由演化半变分不等式和 Banach 空间中的一个分数阶微分方程组成。利用Rothe方法和满射性结果，我们推导出该问题在某些温和条件下存在唯一解。此外，我们使用完全离散的方案来近似分数微分半变分不等式并提供近似值的误差估计。最后，应用主要结果来获得具有粘附力的粘弹性摩擦接触问题的唯一可解性和数值分析。