Fuzzy differential equations for universal oscillators

This study considers universal oscillator fuzzy differential equations. The differential inclusion method is applied to this problem by considering the universal oscillator fuzzy differential equations as universal oscillator uncertain dynamical systems. Three types of damped oscillators are considered comprising underdamped, critically damped, and overdamped oscillators. The existence and uniqueness of the solutions to each case are discussed and proofs are given under some certain conditions. For universal oscillator uncertain dynamical systems with an undamped forcing function, the existence and uniqueness of the solutions and big solutions are also verified, while the scopes of the trajectories to the solutions are obtained based on the inclusion relationship between solutions and big solutions. We also prove the existence and uniqueness of solutions to universal oscillator uncertain dynamical systems with a damped forcing function by using other more direct conditions.