Stability results for a new kind fractional partial differential variational inequalities

This paper is devoted to the study of the stability result of a fractional partial differential variational inequality (FPDVI, for short), which is composed of a fractional evolution equation and a time-dependent variational inequality. The perturbation problem of FPDVI is that the mapping and the constraint set are perturbed by two different parameters. Employing advanced theory of non-smooth analysis, we present the closedness and the upper semicontinuity of the mild solution set mapping for the perturbation problem. Furthermore, we derive the continuity result. Finally, via employing the Ascoli-Arzelà theorem and Kolmogorov-Riesz-Frechét theorem, the stability result is illustrated by a specific numerical example.