Generalized linear differential equation using Hyers-Ulam stability approach

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...

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Bibliographic Details
Published in:AIMS mathematics Vol. 6; no. 2; pp. 1607 - 1623
Main Authors: Unyong, Bundit, Govindan, Vediyappan, Bowmiya, S., Rajchakit, G., Gunasekaran, Nallappan, Vadivel, R., Peng Lim, Chee, Agarwal, Praveen
Format: Journal Article
Language:English
Published: AIMS Press 01.01.2021
Subjects:
hyers-ulam stability
linear differential equation
ISSN:2473-6988, 2473-6988
Online Access:Get full text
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Summary: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.
ISSN:2473-6988
2473-6988
DOI:10.3934/math.2021096