Generalized Linear Differential Equation using Hyers - Ulam Stability Approach
DOI:
https://doi.org/10.29020/nybg.ejpam.v17i4.5445Keywords:
Hyers-Ulam Stability, Differential equationAbstract
In this paper, We demonstrate the Hyers - Ulam stability of linear differential equation of fourth order. We interact with the differential equation
\begin{align*}
\gamma^{iv} (\omega) + \rho_1 \gamma{'''} (\omega)+ \rho_2 \gamma{''} (\omega) + \rho_3 \gamma' (\omega) + \rho_4 \gamma(\omega) = \chi(\omega),
\end{align*}
where $\gamma \in c^4 [\alpha,\beta], \chi \in [\alpha,\beta]$. 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.
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Copyright (c) 2024 S. Bowmiya, G. Balasubramanian, Vediyappan Govindan, Mana Donganont, Haewon Byeon
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