General formulas for solution some important partial differential equations using El-Zaki transform

Document Type : Research Paper

Authors

Department of mathematics, Faculty of Education for girls, University of Kufa, Najaf 54002, Iraq

Abstract

Our aim in this work, general formula for solution some partial differential equations are derived, which have applications in other sciences. Elzaki transformation was used to obtain these formulas. Moreover, some examples are solved using these formulas.

Keywords

[1] S.A.S. Al-Sook and M.M. Amer, Laplace–Elzaki transform and its properties with applications to integral and
partial differential equations, Journal of Natural Sciences, Life Appl. Sci. 3(2) (2019) 96–110.
[2] M.A. Asiru, Application of the Sumudu transform to discrete dynamic systems, Int. J. Math. Educat. Sci. Tech.
3 (2003).
[3] A. Atangana and A. Kilicman, A novel integral operator transform and its application to some FODE and FPDE
with some kind of singularities, Math. Prob. Engin. 12(1) (2013).
[4] N. Athraa and M. Ali, Solving Euler’s equation by using new transformation, J. Karbala Univ. 6 (2008).
[5] T.M. Elzaki, On the connections between Laplace and Elzaki transforms, Adv. Theor. Appl. Math. 6(1) (2011)
1–11.
[6] T.M. Elzaki and S.M. Ezaki, Application of new transform ”Elzaki Transform” to partial differential equations,
Global J. Pure Appl. Math. 7(1) (2011) 65–70.[7] A. Hassan and A. Neamah, On solutions of differential equations by using laplace transformation, J. Islamic Univ.
3 (2010).
[8] H.N. Kadhim, A.N. ALbukhuttar and M.S. ALibrahimi, Novel transform for solving Euler-Cauchy equation, J.
Interdiscip. Math. 24(7) (2021).
[9] X. Liang, F. Gao, Y.-N. Gao, X.-J. Yang, Applications of a novel integral transform to partial differential equations,
J. Nonlinear Sci. Appl. 10(2) (2017).
[10] R. Murray, Theory and Problems of Laplace Transform, New York, USA: Schaum’s Outline Series, McGraw-Hill,
1965.
[11] S. Sharma and A.J. Obaid, Mathematical modelling, analysis and design of fuzzy logic controller for the control
of ventilation systems using MATLAB fuzzy logic toolbox, J. Interdiscip. Math. 23(4) (2020) 843–849.
[12] M.E. Slaminasab and S.A. Bandy, Study on usage of Elzaki transform for the ordinary differential equations with
non-constant coefficients, Int. J. Ind. Math. 7 (2015).
[13] D. Verma, Applications of laplace transformation for solving various differential equations with variable coefficients, Int. J. Innov. Res. Sci. Tech. 4 (2018).
Volume 13, Issue 1
March 2022
Pages 3181-3190
  • Receive Date: 01 November 2021
  • Revise Date: 30 November 2022
  • Accept Date: 29 December 2022