This study focuses on analyzing the hyper-order associated with meromorphic solutions of nonlinear complex differential equations represented by 𝒫[𝒈] – Q𝒈γ𝒫 = R, where 𝒫[𝒈] denotes a differential polynomial in 𝒈, γ𝒫 indicates for the degree of 𝒫[𝒈], and the coefficients of 𝒫[𝒈], along with Q = Q(z) and R = R(z), satisfy certain prescribed growth conditions.