Document Type : Research Paper


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


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 .


Main Subjects

  • Barnes, B. (2016). Polynomial integral transform for solving differential equations.  J. Pure Appl. Math9(2), 140-151.
  • Aboodh, K. S. (2013). The new integral transform, ”Aboodh transform”.  Pure Appl. Math9(1), 35-43.
  • Braun, M. (1993). Differential Equation and Their Application, 4th Ed, New York, Springer-Verlag.
  • Mansour, E. A., Mehdi, S. A., & Kuffi, E. A. (2021). The new integral transform and its applications. J. Nonlinear Anal. Appl12(2), 849-856.
  • Mohmmed, A. H., & Kathem, A. N. (2008). Solving Euler’s equation by using new transformation. Kerbala Univ6(4), 103-109.
  • Zaki, T. M. (2011). The new integral transform, ”Elzaki transform”. J. Pure. Appl. Math7(1), 57-64.
  • Kuffi, E. A., & Maktoof, S. F. (2021). A new general polynomial transforms for solving ordinary differential equations with variable coefficients. International Journal of Nonlinear Analysis and Applications12(Special Issue), 2189-2196.
  • Düz, M., Issa, A., & Avezov, S. (2022). A new computational technique for Fourier transforms by using the Differential transformation method. Bulletin of International Mathematical Virtual Institute12(2), 287-295.
  • Maktoof, S. F., Kuffi, E., & Abbas, E. S. (2021). “Emad-Sara Transform” a new integral transform. Journal of Interdisciplinary Mathematics24(7), 1985-1994.
  • Kayabaşı, H., Düz, M., & Issa, A. (2022). The variational iteration method for solving second order linear non-homogeneous differential equations with constant coefficients. Romanian Mathematical Magazine13(2), 1-5.
  • Khan, Z. H., & Khan, W. A. (2008). N-transform properties and applications. NUST journal of engineering sciences1(1), 127-133.