Generalized linear differential equation using Hyers-Ulam stability approach

Bundit Unyong; Vediyappan Govindan; S. Bowmiya; G. Rajchakit; Nallappan Gunasekaran; R. Vadivel; Chee Peng Lim; Praveen Agarwal; Bundit Unyong; Vediyappan Govindan; S. Bowmiya; G. Rajchakit; Nallappan Gunasekaran; R. Vadivel; Chee Peng Lim; Praveen Agarwal

doi:10.3934/math.2021096

AIMS Mathematics

2021, Volume 6, Issue 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

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.
- Hyers-Ulam Stability,
- linear differential equation
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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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., $ \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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