A Further Generalization of the General Polynomial Transform and its Basic Characteristics and Applications

Issa, Ahmad; Kuffi, Emad; Duz, Murat

doi:10.37652/juaps.2023.143479.1140

	A Further Generalization of the General Polynomial Transform and its Basic Characteristics and Applications
Journal of University of Anbar for Pure Science
Article 41, Volume 17, Issue 2, December 2023, Pages 338-342 PDF (560.41 K)
Document Type: Research Paper
DOI: 10.37652/juaps.2023.143479.1140
Authors
Ahmad Issa^* ¹; Emad Kuffi²; Murat Duz³
¹Faculty of Science, Karabuk University, Karabuk, Turkiye.
²Al-Qadisiyah University/ College of Engineering.
³Karabuk University, Faculty of Science, Department of Mathematics,Turkey
Abstract
In this article , we developed the general polynomial transform into a new transform ( Ahmad - Emad - Murat transform ) , which was expanded by writing a general formula of the Kernel function K ( x , t ) . Besides , we presented the essential characteristics and theorems of AEM transform and made new results. In addition , the efficiency of the proposed transform was verified by applying it to a set of important examples , the most important one is “ Cauchy Euler problems ” . The main advantage of the proposed transform is getting a more generalized transform and making it easier to handle in solving differential equations with variable coefficients , reducing effort and time in the calculations . Hence , the polynomial integral transform and general polynomial transform that have been introduced during the last years are special transforms of the AEM transform .
Keywords
General Polynomial Transform,,; ,،AEM Transform,,; ,،differential equations

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