Generalized linear differential equation using hyers-ulam stability approach

In this paper, we study the Hyers-Ulam stability with respect to the linear differential condition of fourth order. Specifically, we treat ψ as an interact arrangement of the differential condition, i.e., ψ^iv (κ) + ξ₁ ψ^′′′ (κ) + ξ₂ ψ^′′ (κ) + ξ₃ ψ^′ (κ) + ξ₄ ψ(κ) = Ψ(κ) where ψ ∈ c⁴ [ℓ, µ], Ψ ∈ [ℓ, µ]. We demonstrate that ψ^iv (κ)+ξ₁ ψ^′′′ (κ)+ξ₂ ψ^′′ (κ)+ξ₃ ψ^′ (κ)+ξ₄ ψ(κ) = Ψ(κ) has the Hyers-Ulam stability. Two examples are provided to illustrate the usefulness of the proposed method.