Solution method for fifth-order fuzzy initial value problem

Fuzzy differential equations (FDEs) are the general concept of ordinary differential equations. FDE seems to be a natural way to model the propagation of cognitive uncertainty in dynamic environments. This article establishes the characteristics of the strongly generalized Hukuhara differentiability (SGHD)-based fifth-order derivative of the fuzzy-valued function (FVF). The Laplace operator is used in SGHD to create a strategy for solving the fifth-order fuzzy initial value problem (FIVP). Furthermore, some examples of FIVP are addressed to exploit liability and the efficiency of our proposed method. Furthermore, the switching points and solutions of FIVP are presented graphically to demonstrate and corroborate the theoretical findings. Additionally, an application of a mass-spring-damper system is solved by our proposed method.