(untitled) (European Journal of Pure and Applied Mathematics, 2024)
In this paper, we study the Hyers-Ulam stability for the fifth-order linear differential equation. In particular, we treat as an arrangement of differential equation and in the form %equation* ^v(x)+η_1^iv(x)+η_2^’’’(x)+η_3^’’(x)+η_4^’(x)+η_5(x)=Ω(x) %equation* where c^5 [k, l], Ω [k, l]. We demonstrate that ^v(x)+η_1^iv(x)+η_2^’’’(x)+η_3^’’(x)+η_4^’(x)+η_5(x)=Ω(x) has the Hyers-Ulam stability. Two illustrative examples are given to represent the effectiveness of the proposed method. Fifth-order linear differential equations find applications in a wide range of fields, from engineering and control theory to physics, biology, and beyond. These equations are powerful tools for modeling systems with complex dynamics that involve multiple interacting forces or rates of change. Understanding and analyzing their stability and behavior can lead to significant advancements in the design, control, and optimization of these systems.