Generalization to The AMK Integral Transform and Its Applications

Salman, Mohanad Faisal; Zhao, Qin

doi:10.37652/juaps.2025.155252.1337

	Generalization to The AMK Integral Transform and Its Applications
Journal of University of Anbar for Pure Science
Volume 19, Issue 1 - Serial Number 19, May and June 2025, Pages 317-321 PDF (673.5 K)
Document Type: Research Paper
DOI: 10.37652/juaps.2025.155252.1337
Authors
Mohanad Faisal Salman^* ; Qin Zhao
School of Mathematics and Statistics, Wuhan University of Technology, Wuhan, China.
Abstract
Since the proposal of Laplace to integral transformation in 1780, many integral transformations have been proposed. Some are based on Laplace, and others are totally independent. Integral transformations play an essential role in solving versatile problems related to various fields due to their phenomenal ability to transform complex problems from one domain (their original domain) to another, where they can be solved and manipulated much more smoothly and easily. The results could be left in their alternative domain or transformed back via the inverse of that integral transformation into their original domain. This article proposes a novel type of integral transformation. Defined within the interval [0, π/2] and utilizing trigonometric function kernels f(ρ) and g(ρ), this new transformation is explored through its basic theorems, properties, and derivatives. The properties of the proposed integral transformation have been successfully and efficiently employed to find exact solutions for specific types of ordinary linear differential equations of the first and second order, expressed in terms of (sin(N)).
Keywords
Integral Transforms; AMK-Transform; Ordinary Differential Equations

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