Generalized linear differential equation using Hyers-Ulam stability approach

Abstract

In this paper, we study the Hyers-Ulam stability with respect to the linear differential condition of fourth order. Specifically, we treat ${\psi}$ as an interact arrangement of the differential condition, i.e., where ${\psi} \in c^4 [{\ell}, {\mu}], {\Psi} \in [{\ell}, {\mu}]$. We demonstrate that ${\psi}^{iv} ({\varkappa}) + {\xi}_1 {\psi}{'''} ({\varkappa})+ {\xi}_2 {\psi}{''} ({\varkappa}) + {\xi}_3 {\psi}' ({\varkappa}) + {\xi}_4 {\psi}({\varkappa}) = {\Psi}({\varkappa})$ has the Hyers-Ulam stability. Two examples are provided to illustrate the usefulness of the proposed method.

Keywords

• hyers-ulam stability
• linear differential equation