## 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)
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Document Type: Research Paper | ||

DOI: 10.37652/juaps.2023.143479.1140 | ||

Authors | ||

Ahmad Issa^{*} ^{1}; Emad Kuffi^{2}; Murat Duz^{3}
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^{1}Faculty of Science, Karabuk University, Karabuk, Turkiye. | ||

^{2}Al-Qadisiyah University/ College of Engineering. | ||

^{3}Karabuk 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 | ||

References | ||

*J. Pure Appl. Math*,*9*(2), 140-151.*Pure Appl. Math*,*9*(1), 35-43.*New York, Springer-Verlag*.*J. Nonlinear Anal. Appl*,*12*(2), 849-856.*Kerbala Univ*,*6*(4), 103-109.*J. Pure. Appl. Math*,*7*(1), 57-64.*International Journal of Nonlinear Analysis and Applications*,*12*(Special Issue), 2189-2196.*Bulletin of International Mathematical Virtual Institute*,*12*(2), 287-295.*Journal of Interdisciplinary Mathematics*,*24*(7), 1985-1994.*Romanian Mathematical Magazine*,*13*(2), 1-5.*NUST journal of engineering sciences*,*1*(1), 127-133.
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