AIMS Mathematics, 2021, 6(2): 1607-1623. doi: 10.3934/math.2021096

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Generalized linear differential equation using Hyers-Ulam stability approach

1 Department of Mathematics, Phuket Rajabhat University, 83000, Phuket, Thailand
2 Department of Mathematics, DMI- St. John the Baptist University, P. O. BOX. 406, Mangochi, Malawi, Central Africa
3 Department of Mathematics, Faculty of Science, Maejo University, Sansai 50290, Chiang Mai, Thailand
4 Department of Mathematical Sciences, Shibaura Institute of Technology, Saitama 337-8570, Japan
5 Institute for Intelligent Systems Research and Innovation, Deakin University, Waurn Ponds, VIC 3216, Australia
6 Department of Mathematics, Anand International College of Engineering, Jaipur, India International Center for Basic and Applied Sciences, Jaipur, 302029, India

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., \begin{align*} {\psi}^{iv} ({\varkappa}) + {\xi}_1 {\psi}{'''} ({\varkappa})+ {\xi}_2 {\psi}{''} ({\varkappa}) + {\xi}_3 {\psi}' ({\varkappa}) + {\xi}_4 {\psi}({\varkappa}) = {\Psi}({\varkappa}) \end{align*} 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.
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