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Generalized linear differential equation using Hyers-Ulam stability approach

  • Received: 22 August 2020 Accepted: 16 November 2020 Published: 25 November 2020
  • MSC : 39B52, 32B72, 32B82

  • 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.

    Citation: Bundit Unyong, Vediyappan Govindan, S. Bowmiya, G. Rajchakit, Nallappan Gunasekaran, R. Vadivel, Chee Peng Lim, Praveen Agarwal. Generalized linear differential equation using Hyers-Ulam stability approach[J]. AIMS Mathematics, 2021, 6(2): 1607-1623. doi: 10.3934/math.2021096

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  • 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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