International Journal of Nonlinear Analysis and Applications

Generalization of Rangaig transform

Document Type : Research Paper

Authors

1 Department of Electrical Technologies, Southern Technical University, Technical Institute Nasiriyah, Iraq

2 Department of Material Engineering, Collage of Engineering, Al-Qadisiyah University, Iraq

Abstract

In this paper, a generalized form of the known Rangaig integral transform has been proposed; the general integral form is presented as a new integral transform called the ``general Rangaig integral transform''. The General Rangaig integral transform has been studied and proven for some fundamental functions, its applicability and ability to find the exact solution have been proven via utilizing the transform in solving first- and second-order ordinary differential equations.

Keywords

[1] E.S. Abbas, E. Kuffi and S.F.M. Al Khozai, Solving an improved heat transmission measuring equation using partial differential equations with variable coefficients, Int. J. Engin. Technol. 7(4) (2018) 5258–5260.
[2] M.A.B. Deakin, Euler’s invention of integral transforms, Arch. Hist. Exact Sci. 33(307) (1985) 307–319.
[3] B.S. Grewal, Higher Engineering Mathematics, 42nd ed. Khanna Publishers, 1998.
[4] H. Jafari, A new general integral transform for solving integral equations, J. Adv. Res. 32 (2021) 133–138.
[5] E. Kreyszig, Advanced Engineering Mathematics, 9th ed., Wiley, 2014.
[6] E.A. Kuffi, A.H. Mohammed, A.Q. Majde and E.S. Abbas, Applying al-Zubair transform on nuclear physics, Int. J. Engin. Technol. Sci. 9(1) (2020) 9–11.
[7] E. Kuffi, E.S. Abbas and S.F. Maktoof, Solving the Beam deflection problem using Al-Tememe transforms, J. Mech. Continua Math. Sci. 14(4) (2019) 519–527.
[8] E. Kuffi, E.S. Abbas and S.O. Mebayet, Al-Tememe transform in solving developed missile automatic control problem, Int. J. Engin. Technol. 7(4) (2018) 6565–6567.
[9] E.A. Mansour, S. Mehdi and E.A. Kuffi, The new integral transform and its applications, Int. J. Nonlinear Anal. Appl. 12(2) (2021) 849–856.
[10] E.A. Mansour, E.A. Kuffi and S.A. Mehdi, The new integral transform “SEE Transform” of Bessel’s functions, Turk. J. Comput. Math. Educ. 12(13) (2021) 3898–3905.
[11] N.A. Rangaig, N.D. Minor, G. Fe, I. Penonal, J.L. Dexter, C. Filipinas, V.C. Convicto, On another type of transform called Rangaig transform, Int. J. Partial Diff. Equ. Appl. 5(1) (2017) 42–48.
[12] L.S. Sawant, Applications of Laplace transform in engineering fields, Int. Res. J. Engin. Technol. 5(5) (2018).
International Journal of Nonlinear Analysis and Applications
Volume 13, Issue 1
March 2022
Pages 2227-2231
  • Receive Date: 07 October 2021
  • Revise Date: 04 November 2021
  • Accept Date: 18 November 2021