This is a preview and has not been published.

Solving the Hotdog Problem by Using the Joint Zero-order Finite Hankel - Elzaki Transform


  • Roqia Khaled Rdwan Department of Mathematics, College of Science, University of Albaath, Homs, Syria.
  • Mohammed Mahmoud Amer Department of Mathematics, College of Science, University of Albaath, Homs, Syria.



Bessel differential operator, Boiling, Cooling, Elzaki transform, Finite Hankel transform, Hotdog, joint zero-order Finite Hankel - Elzaki transform, Partial Differential Equation.


This paper is concerned with combining two different transforms to present a new joint transform FHET and its inverse transform IFHET. Also, the most important property of FHET was concluded and proved, which is called the finite Hankel – Elzaki transforms of the Bessel differential operator property, this property was discussed for two different boundary conditions, Dirichlet and Robin. Where the importance of this property is shown by solving axisymmetric partial differential equations and transitioning to an algebraic equation directly. Also, the joint Finite Hankel-Elzaki transform method was applied in solving a mathematical-physical problem, which is the Hotdog Problem. A steady state which does not depend on time was discussed for each obtained general solution, i.e. in the boiling and cooling states. To clarify the idea of temperature rise and fall over the time domain given in the problem, some figures were drawn manually using Microsoft PowerPoint. The obtained results confirm that the proposed transform technique is efficient, accurate, and fast in solving axisymmetric partial differential equations.


Download data is not yet available.


Debnath L, Bhatta D. Integral Transforms and Their Applications. 3rd ed. New York, USA: CRC Press; 2015. Chapter 13, Finite Hankel Transform; p. 501-511. .

Hasan SK, Sameer QH. On Comparison Study Between Double Sumudu and Elzaki Linear Transforms Method for Solving Fractional Partial Differential Equations. Baghdad Sci J. 2021 Feb 9; 18(3): 509-521.

Elzaki TM. The New Integral Transform ''ELzaki Transform''. Glob J Pure Appl Math. ISSN 0973-1768, 2011; 7(1): 57-64. Available from:

Athraa NA, Yasmin AA. Using the Elzaki Transform to Solve Systems of Partial Differential Equations. Eurasian J phys chem Math. 2795-7667. 2022 Apr; 5:1-11.

Myasar OE, Luma NMT. New Approach for Solving Three Dimensional Space Partial Differential Equation. Baghdad Sci J. 2019 Sep 23; 16(3):786-792.

Hassan M, Elzaki TM. Double Elzaki Transform Decomposition Method for Solving Non-Linear Partial Differential Equations. J appl math phys. 2020; 8(8): 1463-1471.

Ahmed SA, Elzaki TM, Hassan AA. Solution of Integral Differential Equations by New Double Integral Transform (Laplace–Sumudu Transform). Abstr Appl Anal. 2020; 2020: 7.

Ahmed SA, Elzaki TM, Elbadri M, Mohamed MZ. Solution of Partial Differential Equations by New Double Integral Transform (Laplace - Sumudu Transform). Ain Shams Eng J. 2021; 12(4): 4045–4049.

Elzaki TM, Ahmed SA, Areshi M, Chamekh M. Fractional Partial Differential Equations and Novel Double Integral Transform. J King Saud Univ Sci. 2022; 34(3): 101832.

Elzaki TM, Ishag AA. Solution of Telegraph Equation by Elzaki-Laplace Transform. African J Eng Technol. 2022; 2(1): 1-7.

Elzaki TM, Alderremy AA. On the New Double Integral Transform for Solving Singular System of Hyperbolic Equations. J Nonlinear Sci Appl. 2018; 11(10): 1207–1214.

Osman WM, Elzaki TM, Siddig NAA. Modified Double Conformable Laplace Transform and Singular Fractional Pseudo-Hyperbolic and Pseudo-Parabolic Equations. J King Saud Univ Sci. 2021; 33: 101378.

Poularikas AD. Transforms and Applications Handbook. New York, USA: CRC Press; 3rd edition. 2010. Chap. 9, p. 1–16. journal homepage:

Mitra A. A Comparative Study of Elzaki and Laplace Transforms to Solve Ordinary Differential Equations of First and Second Order. J Phys: Conf Ser. 2021; 1913: 1-9.