Skripnik N. V.
Ukr. Mat. Zh. - 2018. - 70, № 3. - pp. 412-428
We develop the ideas of the method of averaging for some classes of fuzzy systems (fuzzy differential equations with delay, fuzzy differential equations with pulsed action, fuzzy integral equations, fuzzy differential inclusions and differential inclusions with fuzzy right-hand sides without and with pulsed action).
Ukr. Mat. Zh. - 2014. - 66, № 11. - pp. 1563–1577
We substantiate the possibility of application of the method of averaging on a finite interval to impulsive differential inclusions with fuzzy right-hand sides containing a small parameter. In the case of periodic right-hand sides, it is shown that the estimate can be improved.
Conditions for the Existence of Local Solutions of Set-Valued Differential Equations with Generalized Derivative
Ukr. Mat. Zh. - 2013. - 65, № 10. - pp. 1350–1362
We consider a generalized set-valued differential equation with generalized derivative and prove the theorems on existence and uniqueness of its solution for the cases of interval-valued and set-valued mappings.
Ukr. Mat. Zh. - 2013. - 65, № 1. - pp. 126-142
We give a review of the development of ideas of the averaging method for some classes of set-valued impulsive systems (impulsive differential inclusions, impulsive differential equations and inclusions with Hukuhara derivative, and impulsive fuzzy differential equations and inclusions).
Ukr. Mat. Zh. - 2008. - 60, № 10. - pp. 1326–1337
Some special space of convex compact sets is considered and notions of a derivative and an integral for multivalued mapping different from already known ones are introduced. The differential equation with multivalued right-hand side satisfying the Caratheodory conditions is also considered and the theorems on the existence and uniqueness of its solutions are proved. In contrast to O. Kaleva's approach, the given approach enables one to consider fuzzy differential equations as usual differential equations with multivalued solutions.
Ukr. Mat. Zh. - 2008. - 60, № 9. - pp. 1287–1296
We establish sufficient conditions for the existence of periodic R-solutions of linear differential inclusions with impulses at fixed times.