Title: Mahgoub Transform Method for the Hyers-Ulam Stability of Differential Equations
Montes Taurus J. Pure Appl. Math. / ISSN: 2687-4814
Article ID: MTJPAM-D-22-00031; Volume 4 / Issue 3 / Year 2022, Pages 263-269
Document Type: Research Paper
Author(s): Ponmana Selvan Arumugam a , Sandra Pinelas b
aDepartment of Mathematics, Kings Engineering College, Irungattukottai, Sri Perumbudur, Chennai – 602 117, Tamil Nadu, India
bDepartment of Exact Science and Engineering, Academia Militar, Lisboa, 2720-113, Amadora, Portugal
Received: 19 September 2022, Accepted: 16 December 2022, Published: 4 February 2023.
Corresponding Author: Sandra Pinelas (Email address: firstname.lastname@example.org)
Full Text: PDF
In this paper we prove the Hyers-Ulam stability of general second-order linear differential equations by using Mahgoub integral transform method. Furthermore we provide some examples to illustrate main results.
Keywords: Hyers-Ulam stability, Second-order linear differential equations, Mahgoub integral transformationReferences:
- S. Aggarwal, N. Sharma and R. Chauhan, Solution of linear Volterra integro-differential equations of second kind using Mahgoub transform, Int. J. Latest Tech. Eng. Management Appl. Sci. 7 (5), 173–176, 2018.
- Q. H. Alqifiary and S.-M. Jung, Laplace transform and generalized Hyers-Ulam stability of differential equations, Electron. J. Differ. Equ 2014, 2014; Article ID: 80.
- A. R. Aruldass, D. Pachaiyappan and C. Park, Hyers-Ulam stability of second-order differential equations using Mahgoub transform, Adv. Difference Equ. 2021, 2021; Article ID: 23.
- D. H. Hyers, On the stability of a linear functional equation, Proc. Natl. Acad. Sci. USA 27, 222–224, 1941.
- S.-M. Jung, A. P. Selvan and R. Murali, Mahgoub transform and Hyers-Ulam stability of first-order linear differential equations, J. Math. Inequal. 15 (3), 1201–1218, 2021.
- M. M. A. Mahgoub, The new integral transform “Mahgoub transform”, Adv. Theor. Appl. Math. 11 (4), 391–398, 2016.
- R. Murali, A. P. Selvan and C. Park, Ulam stability of linear differential equations using Fourier transform, AIMS Math. 5 (2), 766–780, 2019.
- R. Murali, A. P. Selvan, C. Park and J. R. Lee, Aboodh transform and the stability of second order linear differential equations, Adv. Difference Equ. 2021, 2021, Article ID: 296.
- M. Oboza, Hyers stability of the linear differential equation, Rocznik Nauk.-Dydakt. Prace Mat. 13, 259–270, 1993.
- M. Oboza, Connections between Hyers and Lyapunov stability of the ordinary differential equations, Rocznik Nauk.-Dydakt. Prace Mat. 14, 141–146, 1997.
- J. M. Rassias, On approximately of approximately linear mappings by linear mappings, J. Funct. Anal. 46, 126–130, 1982.
- J. M. Rassias, R. Murali and A. P. Selvan, Mittag-Leffler-Hyers-Ulam stability of linear differential equations using Fourier transforms, J. Comput. Anal. Appl. 29 (1), 68–85, 2021.
- Th. M. Rassias, On the stability of the linear mappings in Banach spaces, Proc. Amer. Math. Soc. 72, 297–300, 1978.
- H. Rezaei, S.-M. Jung and Th. M. Rassias, Laplace transform and Hyers-Ulam stability of linear differential equations, J. Math. Anal. Appl. 403 (1), 244–251, 2013.
- S. M. Ulam, Problem in modern mathematics, Chapter IV, Science Editors, Willey, New York, 1960.
- G. Wang, M. Zhou and L. Sun, Hyers-Ulam stability of linear differential equations of first order, Appl. Math. Lett. 21 (10), 1024–1028, 2008.