S. Ponnurangan - Department of Mathematics, Sri Vidya Mandir Arts and Science College, Katteri, Uthangarai 636902, India. M. Angayarkanni - Department of Mathematics, Kandaswami Kandra's College, P. Velur 638182, India. H. Byeon - Department of AI-Big Data, College of AI Convergence, Inje University, Gimhae, S. Korea. V. Govindan - Department of Mathematics, Hindustan Institute of Technology and Science, Chennai 603103, India. H. Ahmad - Section of Mathematics, International Telematic University Uninettuno, Corso Vittorio Emanuele II, 39,00186 Roma, Italy. S. El-Morsy - Department of Mathematics, College of Science and Arts, Al- Badaya 51951, Qassim University, Saudi Arabia. - Basic Science Department, Nile Higher Institute for Engineering and Technology, Mansoura, Egypt.
In this manuscript, we discusses the Kamal transform for homogeneous and non-homogeneous linear differential equations. Using this unique integral transform, we resolve higher-order linear differential equations. Alternatively, it can produce the conditions required for Hyers-Ulam stability by using the Kamal transform. This is the first attempt to use the Kamal transform to show that a linear differential equation is stable. The Kamal transform method is more useful for investigating the stability problem for differential equations with constant coefficients, as this study also shows. The discussion of applications follows to illustrate our approach. In other words, we establish sufficient with a constant coefficient by using the Kamal transform method. Moreover, this paper provides a new method to investigate the stability of differential equations. Further, this paper shows that the Kamal transform method is more convenient for investigating stability problems for linear differential equations with a constant coefficient.
S. Ponnurangan, M. Angayarkanni, H. Byeon, V. Govindan, H. Ahmad, S. El-Morsy, Kamal transform and Ulam stability of \(\varphi^{\rm th}\) order linear differential equations, Journal of Mathematics and Computer Science, 33 (2024), no. 2, 189--203
Ponnurangan S., Angayarkanni M., Byeon H., Govindan V., Ahmad H., El-Morsy S., Kamal transform and Ulam stability of \(\varphi^{\rm th}\) order linear differential equations. J Math Comput SCI-JM. (2024); 33(2):189--203
Ponnurangan, S., Angayarkanni, M., Byeon, H., Govindan, V., Ahmad, H., El-Morsy, S.. "Kamal transform and Ulam stability of \(\varphi^{\rm th}\) order linear differential equations." Journal of Mathematics and Computer Science, 33, no. 2 (2024): 189--203
