(untitled) (European Journal of Pure and Applied Mathematics, 2024)
In this paper, We demonstrate the Hyers - Ulam stability of linear differential equation of fourth order. We interact with the differential equation align* γ^iv (ω) + ρ_1 γ’’’ (ω)+ ρ_2 γ’’ (ω) + ρ_3 γ’ (ω) + ρ_4 γ(ω) = χ(ω), align* where γ c^4 [α,β], χ [α,β]. Hyers-Ulam stability concerns the robustness of solutions of functional equations under small perturbations, ensuring that a solution approximately satisfying the equation is close to an exact solution. We extend this concept to fourth-order linear differential equations and continuous functions. Using fixed-point methods and various norms, we establish conditions under which such equations exhibit Hyers-Ulam stability. Several illustrative examples are provided to demonstrate the application of these results in specific cases, contributing to the growing understanding of stability in higher-order differential equations. Our findings have implications in both theoretical research and practical applications in physics and engineering.