Full averaging scheme for impulsive differential inclusions with fuzzy right-hand side in terms of R-solutions

Abstract

In the works of T. A. Komleva, A. V. Plotnikov, L. I. Plotnikova the possibility of applying the averaging method on a finite interval for differential inclusions with a fuzzy right-hand side containing a small parameter in terms of solution sets (with a transition to separate $\alpha$-solutions in the proof), and in the works of N. V. Skripnik similar results were obtained for impulse differential inclusions with a fuzzy right-hand side. Later in the works of T. A. Komleva and A. V. Plotnikov the concept of $R$-solution of the differential inclusion with a fuzzy right-hand side was introduced and the possibility of applying the averaging method in terms of $R$-solutions was justified (without passing to $\alpha$-solutions in the proof). In this article, these results are transferred to the impulse case, namely, the concept of $R$-solution is introduced and the possibility of using the full averaging scheme for impulse differential inclusions with a fuzzy right-hand side in terms of $R$-solutions is substantiated.