تحويل HK: طريقة مبنية على تحويل لابلاس لحل مسائل النمو والاضمحلال السكاني

[1] D. G. Zill, “A First Course in Differential Equations with Modeling Applications,” p. 426, 2009, doi: 978-1111827052.

[2] J. J. T. .Kilbas, Anatoly A, Hari M . Srivastava, Theory and applications of fractional differential equations. 2000.

[3] W. T. Coffey and Y. P. Kalmykov, The langevin equation: With applications to stochastic problems in physics, chemistry and electrical engineering. 2012. doi: 10.1142/10490.

[4] D. P. Patil, D. S. Shirsath, and V. S. Gangurde, “Application of Soham Transform in Newtons Law of Cooling,” Int. J. Res. Eng. Sci., vol. 10, no. 6, pp. 1299–1303, 2022.

[5] K. R. T. Arts, B. H. Commerce, and A. M. S. College, “Applications of the HY Transform for Newton ’ s Law of Cooling,” vol. 9, no. 2, pp. 740–745, 2022.

[6] D. P. Patil, P. R. Pardeshi, R. A. Shaikh, and H. M. Deshmukh, “Applications of Emad Sara transform in handling population growth and decay problems,” Int. J. Creat. Res. Thoughts, vol. 10, no. 7, pp. a137–a141, 2022, [Online]. Available: https://ijcrt.org/papers/IJCRT2207013.pdf

[7] H. Hilmi, S. J. MohammedFaeq, and S. S. Fatah, “Exact and Approximate Solution of Multi-Higher Order Fractional Differential Equations Via Sawi Transform and Sequential Approximation Method,” J. Univ. BABYLON Pure Appl. Sci., vol. 32, no. 1, pp. 311–334, Mar. 2024, doi: 10.29196/jtxxvm65.

[8] M. E. H. Attaweel, H. A. A. Almassry, and S. F. Khyar, “A New Application of Sawi Transform for Solving Volterra Integral Equations and Volterra Integro-differential Equations,” vol. 2, pp. 65–77, 2019.

[9] A. Turab, H. Hilmi, J. L. G. Guirao, S. Jalil, N. Chorfi, and P. O. Mohammed, “The Rishi Transform method for solving multi-high order fractional differential equations with constant coefficients,” AIMS Math., vol. 9, no. 2, pp. 3798–3809, 2024, doi: 10.3934/math.2024187.

[10] R.kumar, J.Chandel, and S.Aggarwal, “A New Integral Transform ‘Rishi Transform’ with Application,” J. Sci. Res., vol. 14, no. 2, pp. 521–532, 2022, doi: 10.3329/jsr.v2i3.4899.

[11] R. W. Smith and C. Fleck, “Derivation and Use of Mathematical Models in Systems Biology,” Pollen Tip Growth From Biophys. Asp. to Syst. Biol., pp. 339–367, Jun. 2017, doi: 10.1007/978-3-319-56645-0_13.

[12] R. M. Sibly and J. Hone, “Population growth rate and its determinants: An overview,” Philos. Trans. R. Soc. B Biol. Sci., vol. 357, no. 1425, pp. 1153–1170, 2002, doi: 10.1098/rstb.2002.1117.

[13] D. P. Patil, P. Nikam, S. Shirsath, and A. N. Aher, “‘ Kushare Transform ’ for Solving the Problems on Growth and Decay,” J. Emerg. Technol. Innov. Res., vol. 9, no. May, pp. 317–323, 2022.

[14] D. P. Patil, M. Y. Paradhi, and P. S. Pansare, “Rangaig integral transform for handling exponentialgrowth and decay problems .,” Int. J. Res. Anal. Rev., vol. 10, no. 1, pp. 200–208, 2023.

[15] E. A. Mansour and E. A. Kuffi, “On the Application of the Emad-Sara Transform Technique to the Solution of Complex Differential Equations,” BIO Web Conf., vol. 97, pp. 1–6, 2024, doi: 10.1051/bioconf/20249700167.

[16] R. Fadhil Mahmood, S. Sidiq Hama, S. Swara Fatah, and H. Hilmi, “Using Kharrat-Toma transform to solve a growth and decay problem,” Tikrit J. Pure Sci., vol. 29, no. 6, pp. 70–79, 2024, doi: https://doi.org/10.25130/tjps.v29i6.1685.

[17] D. P. Patil, B. S. Patel, and P. S. Khelukar, “Applications of Alenezi Transform for handling Exponential growth and Decay Applications of Alenezi Transform for handling Exponential growth and Decay Problems,” no. July, 2022.

[18] H. Hilmi, S. Jalil, H. H. Rahman, and B. M. Faraj, “Leveraging the Anuj transform: A novel approach to modeling population dynamics in interdisciplinary sciences,” Al-Jabar J. Pendidik. Mat., vol. 15, no. 2, pp. 645–653, 2024, doi: 10.24042/ajpm.v15i2.23494.

[19] R. O. Mustafa, B. K. Mohammed, H. F. Mahmood, S. A. Ahmad, and H. D. M. Hilmi, “Predictive Modeling of Compressive Strength of POFA-Enhanced Self-Compacting Concrete Using LR, NLR, and ANN,” Comput. Eng. Phys. Model., 2025, doi: 10.22115/cepm.2025.537678.1372.

[20] M. C. Singh, A. Prashar, J. Singh, and S. Kumar, “Reservoir capacity loss and sedimentation assessment of Dholbaha dam located in Punjab, India using remote sensing and bathymetric survey techniques,” Water Pract. Technol., vol. 18, no. 11, pp. 2901–2922, 2023, doi: 10.2166/wpt.2023.188.

[21] 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.

[22] H. D. Rozenfeld, D. Rybski, J. S. Andrade, M. Batty, H. E. Stanley, and H. A. Makse, “Laws of population growth,” Proc. Natl. Acad. Sci. U. S. A., vol. 105, no. 48, pp. 18702–18707, 2008, doi: 10.1073/pnas.0807435105.

[23] 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.pdf,” Basrah J. Sci., vol. 43, no. 1, pp. 86–99, 2025, doi: 10.29072/basjs.20250106.

[24] H. Hilmi, K. Hama Faraj Jwamer, S. Ali Saleh Al-Joufi, S. Jalil, H. Hussein Rahman, and S. Swara Fatah, “A New Integral Transform ‘Dukani Transform’ with Applications,” J. Al-Qadisiyah Comput. Sci. Math., vol. 16, no. 4, pp. 1–13, Dec. 2024, doi: 10.29304/jqcsm.2024.16.41793.

[25] R. Gupta, R. Gupta, and D. Verma, “Application of Novel Integral Transform: Gupta Transform To Mechanical and Electrical Oscillators,” ASIO J. Chem. Physics, Math. Appl. Sci., vol. 4, no. 1, pp. 04–07, 2020, doi: 10.2016-28457823.

[26] 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.

[27] D. P. Patil, S. Borse, and D. Kapadi, “Applications of Emad Falih Transform For General Solution of Telegraph equation,” Int. Adv. Res. J. Sci. Eng. Technol., vol. 9, no. 6, pp. 19450-19454., 2022.

[28] S. Aggarwal, S. D. Sharma, and A. R. Gupta, “A New Application of Mohand Transform for Handling Abel ’ s Integral Equation,” J. Emerg. Technol. Innov. Res., vol. 6, no. 3, pp. 600–608, 2019.

[29] 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.

[30] Murray R.Spiegel, Schaums’s -Laplace Transforms. United states: Mcgraw Hill, 1965.

[31] Joel L. Schiff, The Laplace Transform Theorey and Applications, vol. 62, no. C. New York: Springer, 1975. doi: 10.1016/S0079-8169(08)61546-9.

[32] S. Aggarwal and G. P. Singh, “Sawi Transform for Population Growth and Decay Problems,” Int. J. Latest Technol. Eng. Manag. Appl. Sci., vol. VIII, no. VIII, pp. 157–162, 2019.