Two-point boundary value problems of uncertain dynamical systems

Recent research shows that in many cases there are no solutions (periodic solutions, etc.) to fuzzy two-point boundary value problems in the sense of H-derivatives. To overcome the disadvantage of H-derivatives in studying fuzzy two-point boundary value problems, in this paper we study fuzzy two-point boundary value problems in the sense of differential inclusions, i.e., two-point boundary value problems of uncertain dynamical systems. We obtain the existence and uniqueness of solutions and the existence of periodic solutions to two-point boundary value problems of uncertain dynamical systems. After introducing the concept of big solutions to two-point boundary value problems of undamped uncertain dynamical systems, we establish the existence and uniqueness of big solutions, discuss the relationship between solutions and big solutions and further get a conclusion concerning the solutions of two-point boundary value problems of uncertain dynamical systems.