Applications of the Tarig Transform and Hyers–Ulam Stability to Linear Differential Equations

L. Chitra, K. Alagesan, Vediyappan Govindan, Salman Saleem (), A. Al-Zubaidi and C. Vimala
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L. Chitra: Department of Mathematics, Kandaswami Kandra’s College, Paramathi Velur 638182, Tamil Nadu, India
K. Alagesan: Department of Mathematics, Kandaswami Kandra’s College, Paramathi Velur 638182, Tamil Nadu, India
Vediyappan Govindan: Department of Mathematics, Hindustan Institute of Technology and Science, Rajiv Gandhi Salai (OMR), Padur, Kelambakkam, Chennai 603103, Tamil Nadu, India
Salman Saleem: Department of Mathematics, College of Science, King Khalid University, Abha 61413, Saudi Arabia
A. Al-Zubaidi: Department of Mathematics, College of Science, King Khalid University, Abha 61413, Saudi Arabia
C. Vimala: Department of Mathematics, Periyar Maniammai Institute of Science & Technology, Vallam, Thanjavur 613403, Tamil Nadu, India

Mathematics, 2023, vol. 11, issue 12, 1-25

Abstract: In this manuscript, we discuss the Tarig transform for homogeneous and non-homogeneous linear differential equations. Using this Tarig integral transform, we resolve higher-order linear differential equations, and we produce the conditions required for Hyers–Ulam stability. This is the first attempt to use the Tarig transform to show that linear and nonlinear differential equations are stable. This study also demonstrates that the Tarig transform method is more effective for analyzing the stability issue for differential equations with constant coefficients. A discussion of applications follows, to illustrate our approach. This research also presents a novel approach to studying the stability of differential equations. Furthermore, this study demonstrates that Tarig transform analysis is more practical for examining stability issues in linear differential equations with constant coefficients. In addition, we examine some applications of linear, nonlinear, and fractional differential equations, by using the Tarig integral transform.

Keywords: differential equation; Hyers–Ulam stability (HUS); Tarig transform (search for similar items in EconPapers)
JEL-codes: C (search for similar items in EconPapers)
Date: 2023
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