Power series solutions of fractional Lotka-Volterra equation

Yu, Jicheng; Feng, Yuqiang

doi:10.22034/cmde.2025.61524.2662

فهرست نشریات دارای اعتبار وزارت علوم، تحقیقات و فناوری

تعداد نشریات	45
تعداد شماره‌ها	1,489
تعداد مقالات	18,174
تعداد مشاهده مقاله	58,791,029
تعداد دریافت فایل اصل مقاله	20,264,654

	Power series solutions of fractional Lotka-Volterra equation
Computational Methods for Differential Equations
مقاله 23، دوره 14، شماره 2، تیر 2026، صفحه 869-876 اصل مقاله (445.59 K)
نوع مقاله: Research Paper
شناسه دیجیتال (DOI): 10.22034/cmde.2025.61524.2662
نویسندگان
Jicheng Yu^* ¹؛ Yuqiang Feng²
¹School of Science, Wuhan University of Science and Technology, Wuhan 430081, Hubei, China.
²1. School of Science, Wuhan University of Science and Technology, Wuhan 430081, Hubei, China. 2. Hubei Province Key Laboratory of Systems Science in Metallurgical Process, Wuhan 430081, Hubei, China.
چکیده
In this paper, the power series method is applied to the fractional Lotka-Volterra equation, one of the most famous competition models in demography and economics. We obtain some power series solutions of the governing equation and prove their convergence. In addition, we analyze the various types of competitive roles depicted by this model through the truncated graphs of these power series solutions. From the graphs, we can find that the fractional order affects the speed of population growth or decrease, and this effect can be seen as continuous with respect to the order.
کلیدواژه‌ها
Power series method؛ Fractional differential equations؛ Lotka-Volterra model

مراجع
[1] I. Area, J. Losada, and J. J. Nieto, A note on the fractional logistic equation, Physica A, 444 (2016), 182–187. [2] I. Area and J. J. Nieto, Power series solution of the fractional logistic equation, Physica A, 573 (2021), 125947. [3] I. Area and J. J. Nieto, On the fractional Allee logistic equation in the Caputo sense, Examples Counterexamples, 4 (2023), 100121. [4] S. Das and P. K. Gupta, A mathematical model on fractional Lotka–Volterra equations, J. Theor. Biol., 277(1) (2011), 1–6. [5] M. D’Ovidio and P. Loreti, Solutions of fractional logistic equations by Euler’s numbers, Physica A, 506 (2018), 1081–1092. [6] Y. Q. Feng and J. C. Yu, Lie symmetry analysis of fractional ordinary differential equation with neutral delay, AIMS Math., 6 (2021), 3592-3605. [7] R. Hilfer, Applications of fractional calculus in physics, Singapore: World Scientific, 2000. [8] M. Izadi, S¸. Yu¨zba¸sı, and W. Adel, Accurate and efficient matrix techniques for solving the fractional Lotka–Volterra population model, Physica A, 600 (2022), 127558. [9] K. Jangid, S. D. Purohit, and D. L. Suthar, A note on Lambert’s law involving incomplete I-functions, J. Sci. Arts, 22(1) (2022), 91–96. [10] M. Jornet, Power-series solutions of fractional-order compartmental models, Comp. Appl. Math., 43 (2024), 67. [11] A. R. Kanth and S. Devi, A practical numerical approach to solve a fractional Lotka–Volterra population model with non-singular and singular kernels, Chaos Solitons Fractals, 145 (2021), 110792. [12] A. A. Kilbas, H. M. Srivastava, and J. J. Trujillo, Theory and applications of fractional differential equations, New York: Elsevier, 2006. [13] S. Kumar, R. Kumar, R. P. Agarwal, and B. Samet, A study of fractional Lotka-Volterra population model using Haar wavelet and Adams-Bashforth-Moulton methods, Math. Meth. Appl. Sci., 43(8) (2020), 5564–5578. [14] T. R. Malthus, Population: The First Essay, Ann Arbor, MI: University of Michigan Press, 1959. [15] P. Manohar, L. Chanchlani, V. Kumar, S. D. Purohit, and D. L. Suthar, Fractional Lotka-Volterra equations by fractional reduced differential transform method, Part. Differ. Eq. Appl. Math., 11 (2024), 100816. [16] T. Modis, Technological forecasting at the stock market, Technol. Forecast. Soc., 62(3) (1999), 173–202. [17] M. Ortigueira and G. Bengochea, A new look at the fractionalization of the logistic equation, Physica A, 467 (2017), 554–561. [18] N. Pareek, A. Gupta, D. L. Suthar, G. Agarwal, and K. S. Nisar, Homotopy analysis approach to study the dynamics of fractional deterministic Lotka-Volterra model, Arab J. Basic Appl. Sci., 29(1) (2022), 121–128. [19] I. Podlubny, Fractional differential equations, San Diego: Academic Press, 1999. [20] S. G. Samko, A. A. Kilbas, and O. I. Marichev, Fractional integrals and derivatives: theory and applications, Yverdon: Gordon and Breach Science Publishers, 1993. [21] D. Stutson and A. S. Vatsala, Generalized monotone method for Caputo fractional differential systems via coupled lower and upper solutions, Dynam. Syst. Appl., 20(4) (2011), 495. [22] P. F. Verhulst, Notice sur la loi que la population suit dans son accroissement, Corr. math. phys., 10 (1838), 113–121. [23] B. J. West, Exact solution to fractional logistic equation, Physica A, 429 (2015), 103–108. [24] J. C. Yu and Y. Q. Feng, Lie symmetry analysis and exact solutions of space-time fractional cubic Schrödinger equation, Int. J. Geom. Methods M., 19 (2022), 2250077. [25] J. C. Yu, Lie symmetry analysis of time fractional Burgers equation, Korteweg-de Vries equation and generalized reaction-diffusion equation with delays, Int. J. Geom. Methods M., 19 (2022), 2250219. [26] J. C. Yu and Y. Q. Feng, Group classification of time fractional Black-Scholes equation with time-dependent coefficients, Fract. Calc. Appl. Anal., 27 (2024), 2335–2358. [27] J. C. Yu and Y. Q. Feng, Lie symmetry, exact solutions and conservation laws of some fractional partial differential equations, J. Appl. Anal. Comput., 13 (2023), 1872-1889. [28] J. C. Yu and Y. Q. Feng, On the generalized time fractional reaction–diffusion equation: Lie symmetries, exact solutions and conservation laws, Chaos Solitons Fractals, 182 (2024), 114855. [29] Z. Y. Zhang and G. F. Li, Lie symmetry analysis and exact solutions of the time-fractional biological population model, Phys. A, 540 (2020), 123134.
آمار تعداد مشاهده مقاله: 243 تعداد دریافت فایل اصل مقاله: 296

سامانه مدیریت نشریات علمی. قدرت گرفته از سیناوب

پیوندهای مفید

آمار

Power series solutions of fractional Lotka-Volterra equation