Application of the SEE transform with the Adomian decomposition method to a nonlinear tumor growth model

Ahmed Fadhil Noaman; Zaid Adil Abdalkareem; Bareq Baqi Salman

doi:10.46481/jnsps.2026.3598

Authors

Ahmed Fadhil Noaman
Department of Mathematics, First Karkh Education Directorate, Ministry of Education, Baghdad, Iraq
Zaid Adil Abdalkareem
[email protected]

Department of Mathematics, First Karkh Education Directorate, Ministry of Education, Baghdad, Iraq
Bareq Baqi Salman
Al-Rusafa Third Education Directorate, Ministry of Education, Baghdad, Iraq

Keywords:

SEE integral technique, Tumor growth, Analytical solution, Mathematical modeling, Adomian decomposition method

Abstract

This study examines the combination of the Sadiq-Emad-Eman (SEE) integral transform and the Adomian decomposition method (ADM) for solving a nonlinear tumor growth model. The combined approach provides a direct analytical procedure for obtaining the exact solution of the model. The SEE transform is used because it generalizes several integral transforms and simplifies the required algebraic operations. The ADM is then applied to represent the nonlinear term as a series of Adomian polynomials. The resulting formulation yields the closed-form solution of the tumor growth model and illustrates how the model depends on the initial tumor-cell population, growth rate, and environmental carrying capacity. The results show that the combined SEE--ADM approach offers a simple analytical method for this nonlinear model while preserving its biological interpretation.

Dimensions

REFERENCES

[1] D. Zips, ``Tumour growth and response to radiation'', in Basic Clinical Radiobiology, M. C. Joiner & A. J. van der Kogel (Eds.), CRC Press, Boca Raton, FL, USA, 2018, pp. 81--98. https://doi.org/10.1201/9780429490606.

[2] A. B. Yusuf, R. M. Dima & S. K. Aina, ``Optimized breast cancer classification using feature selection and outliers detection'', Journal of the Nigerian Society of Physical Sciences 3 (2021) 298. https://doi.org/10.46481/jnsps.2021.331.

[3] M. Alsaoudi, G. Gharib, E. A. Kuffi & A. Guiatni, ``A new two-parameter integral transform `MAHA transform' and its applications in real life'', WSEAS Transactions on Mathematics 23 (2024) 536. https://doi.org/10.37394/23206.2024.23.56.

[4] R. A. Deshmukh, V. S. Goswami & D. P. Patil, ``Application of Laplace integral transform in tumor growth model'', Journal of Emerging Technologies and Innovative Research 12 (2025) e354. https://www.jetir.org/papers/JETIR2510448.pdf.

[5] E. A. Kuffi, S. A. Mehdi & E. A. Mansour, ``Color image encryption based on new integral transform SEE'', Journal of Physics: Conference Series 2322 (2022) 012016. https://doi.org/10.1088/1742-6596/2322/1/012016.

[6] E. A. Kuffi & E. A. Mansour, ``Solving partial differential equations using the new integral transform `double SEE integral transform''', Journal of Physics: Conference Series 2322 (2022) 012009. https://doi.org/10.1088/1742-6596/2322/1/012009.

[7] E. A. Mansour, E. A. Kuffi & S. A. Mehdi, ``Applying SEE transform in solving Faltung-type Volterra integro-differential equation of first kind'', Journal of Interdisciplinary Mathematics 25 (2022) 1315. https://doi.org/10.1080/09720502.2022.2040848.

[8] Z. R. Rustam & N. A. Sulaiman, ``SEE transform technique for solving system of linear Volterra integro-differential equations of the second kind'', Polytechnic Journal 12 (2022) 6. https://doi.org/10.25156/ptj.v12n2y2022.pp6-16.

[9] E. A. Mansour & E. A. Kuffi, ``SEE transform in difference equations and differential-difference equations compared with neutrosophic difference equations'', International Journal of Neutrosophic Science 22 (2023) 36. https://doi.org/10.54216/IJNS.220403.

[10] D. Thakur & E. A. Kuffi, ``Exact solutions of cardiovascular models by using Upadhyaya transform'', Journal of Kufa for Mathematics and Computer 11 (2024) 37. https://doi.org/10.31642/JoKMC/2018/110107.

[11] Y. Liu, R. Wu & A. Yang, ``Research on medical problems based on mathematical models'', Mathematics 11 (2023) 2842. https://doi.org/10.3390/math11132842.

[12] V. J. Shaalini & S. E. Fadugba, ``A new multi-step method for solving delay differential equations using Lagrange interpolation'', Journal of the Nigerian Society of Physical Sciences 3 (2021) 159. https://doi.org/10.46481/jnsps.2021.247.

[13] E. A. Mansour, E. A. Kuffi & S. A. Mehdi, ``The new integral transform `SEE transform' and its applications'', Periodicals of Engineering and Natural Sciences 9 (2021) 1016. https://doi.org/10.21533/pen.v9.i2.803.

[14] E. A. Mansour & E. A. Kuffi, ``The utilization of the Emad-Falih integral transformation to solve some cardiovascular models'', Mathematical Applications 12 (2023) 18. https://doi.org/10.13164/ma.2023.120203.

[15] E. A. Mansour & E. A. Kuffi, ``The Mayan transform: a novel integral transform of complex power parameters and applications to neutrosophic functions'', International Journal of Neutrosophic Science 23 (2024) 323. https://doi.org/10.54216/IJNS.230127.

[16] W. Li & Y. Pang, ``Application of Adomian decomposition method to nonlinear systems'', Advances in Difference Equations 2020 (2020) 67. https://doi.org/10.1186/s13662-020-2529-y.

[17] E. A. Mansour, E. A. Kuffi & S. A. Mehdi, ``On the SEE transform and systems of ordinary differential equations'', Periodicals of Engineering and Natural Sciences 9 (2021) 277. https://doi.org/10.21533/pen.v9.i3.845.