Analytical Solutions of Chemical Reaction Kinetic Models Through Integral Transform Techniques

Authors

  • Pshtiwan Salim Mohammed Department of Chemistry, College of Science, Charmo University, Chamchamal, Sulaymaniyah 46023, Iraq
  • Hozan Hilmi Department of Mathematics, College of Science, University of Sulaimani, Sulaymaniyah 46001, Iraq.
  • Shwan Swara Fatah Department of Software Engineering, College of Engineering and Computation Science, Charmo University Chamchamal, Sulaymaniyah 46023, Iraq
  • Bryar Khdhir Abas Department of Mathematics, College of Science, University of Sulaimani, Sulaymaniyah 46001, Iraq

DOI:

https://doi.org/10.56714/bjrs.52.1.10

Keywords:

Chemical Science;, HK transform;, Mathematical Modelling;, Chemical Reaction Kinetic;, Chemical Mixture.

Abstract

Experts in mathematical modeling are currently using integral transforms to model many scientific phenomena. In this sense, the current work evaluates the success rate of the HK transform relative to the well-known Laplace transform by examining how it can be used to solve differential equations describing chemical processes. A first-order differential equation representing chemical reaction and diffusion models was used to demonstrate the HK transform's ability to simplify calculations and yield exact analytical solutions. The same method was then applied to a model that generated component diffusion in a reactive medium with a time-dependent coefficient, demonstrating the transform's ability in handling various coefficients. Lastly, the study examined a single step reversible chemical process represented by a second-order differential equation, and the outcomes of the Laplace and HK transforms were contrasted. The comparison established the HK transform as a trustworthy substitute mathematical tool for modeling and studying a variety of chemical systems by confirming that both transformations provide com-parable accuracy and efficacy.

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References

[1] D. G. Zill, A First Course in Differential Equations with Modeling Applications, 11th ed. ISBN: 978-1-337-29312-9: Cengage Learning, 2009.

[2] W. A.Strauss, Partial Differential Equations, ISBN:97804. 2nd th edition. | Abingdon, Oxon ; New York : Routledge, 2021.: Routledge, 2007.

[3] G. K. Gupta, R. Sacks-Davis, and P. E. Tescher, "A review of recent developments in solving ODEs," ACM Comput. Surv., vol. 17, no. 1, pp. 5–47, Mar. 1985, DOI: 10.1145/4078.4079. DOI: https://doi.org/10.1145/4078.4079

[4] A. M. Wazwaz, A First Course in Integral Equations. ISBN 9789814675116: World Scientificpublishing company, 1997. DOI: https://doi.org/10.1142/3444

[5] H. Hilmi, H. H. Rahman, and S. Jalil, "Rishi Transform to Solve Population Growth and Decay Problems," Basrah J. Sci., vol. 42, no. 2, pp. 207–218, 2024, DOI: 10.29072/basjs.20240204.

[6] R. P. Sharma and S. R. Mishra, "EFFECT OF HIGHER ORDER CHEMICAL REACTION ON MAGNETOHYDRODYNAMIC MICROPOLAR FLUID FLOW WITH INTERNAL HEAT SOURCE," Int. J. Fluid Mech. Res., vol. 47, no. 2, pp. 121–134, 2020, DOI: 10.1615/INTERJFLUIDMECHRES.2019027201. DOI: https://doi.org/10.1615/InterJFluidMechRes.2019027201

[7] A. H. Kamal Sedeeg, "The New Integral Transform' Kamal Transform,'" Adv. Theor. Appl. Math., vol. 11, no. 4, pp. 451–458, 2016.

[8] S. Latif Shaikh, "Introducing a New Integral Transform: Sadik Transform," Am. Int. J. Res. Sci., vol. 22, no. 1, pp. 100–102, 2018, DOI: 10.13140/RG.2.2.25805.08161.

[9] A. I. El-Mesady, Y. S. Hamed, and A. M. Alsharif, "Jafari transformation for solving a system of ordinary differential equations with medical application," Fractal Fract., vol. 5, no. 130, pp. 1–12, 2021, DOI: 10.3390/fractalfract5030130. DOI: https://doi.org/10.3390/fractalfract5030130

[10] Joel L. Schiff, The Laplace Transform Theory and Applications, vol. 62. New York, ISBN: 0-387-98698-7: Springer, 1975.

[11] R. Gupta, R. Gupta, and D. Verma, "Solving Schrodinger Equation for a Quantum Mechanical Particle By a New Integral Transform: Rohit Transform," ASIO J. Chem. Physics, Math. Appl. Sci., vol. 4, no. 1, pp. 32–36, 2020, DOI: 10.2016-53692176.

[12] D. P. Patil, Y. S. Suryawanshi, and M. D. Nehete, "Application of Soham Transform for Solving Mathematical Models Occurring in Health Science and Biotechnology," Int. J. Math. Stat. Oper. Res., vol. 2, no. 2, pp. 273–288, 2022, DOI: 10.47509/IJMSOR.2022.v02i02.11. DOI: https://doi.org/10.47509/IJMSOR.2022.v02i02.11

[13] T. M. Elzaki, "The new integral transform 'Elzaki transform,'" Glob. J. Pure Appl. Math., vol. 7, no. 1, pp. 57–64, 2011.

[14] R. Gupta, R. K. Verma, and S. K. Verma, "Solving Wave Equation and Heat Equation by Rohit Transform (RT)," J. Phys. Conf. Ser., vol. 2325, no. 1, 2022, DOI: 10.1088/1742-6596/2325/1/012036. DOI: https://doi.org/10.1088/1742-6596/2325/1/012036

[15] H. Hussein Rahman, B. Khdhir Abas, H. Hilmi, and S. Jalil Mohamadfaeq, "Modeling and Dynamical System of Iraq's Population Based on Census 2024 and Projections for Future," Basrah J. Sci., vol. 43, no. 1, pp. 86–99, 2025, DOI: 10.29072/basjs.20250106.

[16] A. Atangana and A. Kilicman, "A novel integral operator transform and its application to some FODE and FPDE with some kind of singularities," Math. Probl. Eng., vol. 2013, no. 531984, pp. 1–7, 2013, DOI: 10.1155/2013/531984. DOI: https://doi.org/10.1155/2013/531984

[17] H. Jafari, M. Nazari, D. Baleanu, and C. M. Khalique, "A new approach for solving a system of fractional partial differential equations," Comput. Math. with Appl., vol. 66, no. 5, pp. 838–843, 2013, DOI: 10.1016/j.camwa.2012.11.014. DOI: https://doi.org/10.1016/j.camwa.2012.11.014

[18] H. Hilmi and K. HamaFaraj Jwamer, "A New Integral Transform and Applications: HK-Transform," Zanco J. Pure Appl. Sci., vol. 36, no. 5, pp. 37–46, Oct. 2024, DOI: 10.21271/ZJPAS.36.5.4. DOI: https://doi.org/10.21271/ZJPAS.36.5.4

[19] H. D. M. Hilmi, R. F. Mahmood, S. M. Rasheed, and K. H. F. Jwamer, "New method for solving fractional differential equations: HK transform," Phys. Scr., vol. 100, no. 5, p. 055221, May 2025, DOI: 10.1088/1402-4896/adc8e5. DOI: https://doi.org/10.1088/1402-4896/adc8e5

[20] R. A. Siegel, "A Laplace Transform Technique for Calculating Diffusion Time Lags," Journal of Membrane Science, vol. 26, no. 3. pp. 251–262, 1986. DOI: 10.1016/S0376-7388(00)82110-9. DOI: https://doi.org/10.1016/S0376-7388(00)82110-9

[21] R. Szabó and G. Lente, "Analytical solutions for the rate equations of some two-step kinetic schemes including a reversible first-order later step," J. Math. Chem., vol. 63, no. 5, pp. 1323–1341, May 2025, DOI: 10.1007/s10910-025-01726-9. DOI: https://doi.org/10.1007/s10910-025-01726-9

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Published

30-06-2026

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Vol. 52 No. 1 (2026)

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How to Cite

Analytical Solutions of Chemical Reaction Kinetic Models Through Integral Transform Techniques. (2026). Journal of Basrah Researches (Sciences), 52(1), 123-134. https://doi.org/10.56714/bjrs.52.1.10