Existence of Solutions to Nonlinear Impulsive Fuzzy Differential Equations

Abstract

In this article, we establish the existence and uniqueness of $(c1)$-differentiable and $(c2)$-differentiable solutions to first-order nonlinear impulsive fuzzy differential equations under generalized Hukuhara differentiability using the contraction mappings principle. In particular, $(c1)$-differentiable solutions are written as hyperbolic cosine and sine functions with impulsive terms, which is the main difficulty. An example is provided to prove our results.