Ckrypnyk N. Fuzzy differential equations and inclusions: asymptotic methods

In the thesis the various classes of fuzzy differential equations are considered (with or without impulse effect and with or without delay), the questions of existence of solutions and their continuous dependence on initial condition and right-hand sides are studied, the fuzzy integral equations are considered. Also the possibility of application of the averaging method for these classes of equations is discussed. The different notions of solutions of fuzzy differential inclusion are introduced and the relationship between them is obtained, the theorems of existence and continuous dependence are proved, the possibility of application of various schemes of the averaging method for fuzzy differential inclusions with or without impulses is studied. The concept of generalized derivative for set-valued mappings is introduced, the basic properties of the generalized derivative are studied, the concept of multivalued differential equations with generalized derivative is introduced and some theorems of existence of solutions of such equation in the general case and a few special cases are proved, the theorem of uniqueness of the solution is obtained. This approach is also applied to the fuzzy case - a generalized fuzzy derivative is introduced, fuzzy differential equations with generalized derivative are studied and existence theorem of the solution is proved