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Modeling and analysis of deforestation and pollution dynamics induced by industrialization using the fractal-fractional Atangana-Baleanu derivative | ||
| Journal of Mathematical Modeling | ||
| دوره 14، شماره 2، مرداد 2026، صفحه 407-430 اصل مقاله (2.35 M) | ||
| نوع مقاله: Research Article | ||
| شناسه دیجیتال (DOI): 10.22124/jmm.2025.31414.2822 | ||
| نویسندگان | ||
| Nobin Daimary* ؛ Ranu Paul | ||
| Gauhati University, Assam, India | ||
| چکیده | ||
| This study presents a fractal-fractional model in the Atangana–Baleanu sense to investigate the dynamics of deforestation and pollution driven by industrialization. The model is analyzed for positivity and boundedness, and the existence and uniqueness of its solution are established using fixed-point theory. The system’s equilibrium points are identified, and the threshold parameter $\mathfrak{R_0}$ is determined, with local asymptotic stability confirmed for all equilibria. Sensitivity analysis highlights the key parameters influencing $\mathfrak{R_0}$, while Ulam–Hyers stability ensures robustness of the solution. Lagrangian polynomial interpolation is employed to approximate the solution, and phase portraits along with numerical simulations in Matlab illustrate the model’s dynamic behavior. The results demonstrate that the fractal-fractional approach provides a comprehensive framework for capturing complex environmental interactions, offering valuable insights into the effects of industrialization on deforestation and pollution. | ||
| کلیدواژهها | ||
| Atangana-Baleanu fractal–fractional operator؛ stability؛ Ulam-Hyres stability | ||
| مراجع | ||
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[1] A. Atangana, Fractal-fractional differentiation and integration: connecting fractal calculus and fractional calculus to predict complex system, Chaos Solitons Fract. 102 (2017) 396–406. [2] A.Atangana, D.Baleanu, Newfractional derivatives with nonlocal and non-singular kernel: theory and application to heat transfer model, (2016) arXiv preprint arXiv:1602.03408 . [3] A. Atangana, S. Qureshi, Modeling attractors of chaotic dynamical systems with fractal–fractional operators, Chaos Solitons Fract. 123 (2019) 320–337. [4] M. Awadalla, M. Rahman, F.S. Al-Duais, A. Al-Bossly, K. Abuasbeh, M. Arab, Exploring the role of fractal-fractional operators in mathematical modelling of corruption, Appl. Math. Sci. Eng. 31 (2023) 2233678. [5] M. Caputo, M. Fabrizio, A new definition of fractional derivative without singular kernel, Prog. Fract. Differ. Appl. 1 (2015) 73–85. [6] N. Chitnis, J.M. Cushing, J.M. Hyman, Bifurcation analysis of a mathematical model for malaria transmission, SIAM J. Appl. Math. 67 (2006) 24–45. [7] B. Dubey, B. Das, Models for the survival of species dependent on resource in industrial environ ments, J. Math. Anal. Appl. 231 (1999) 374–396. [8] S. Etemad, I. Avci, P. Kumar, D. Baleanu, S. Rezapour, Some novel mathematical analysis on the fractal–fractional model of the AH1N1/09 virus and its generalized Caputo-type version, Chaos Solitons Fract. 162 (2022) 112511. [9] M. Fahimi, K. Nouri, L. Torkzadeh, Analytical investigation of fractional SEIRVQD measles math ematical model, J. Math. Model. 13 (2025) 393–413. [10] J.F. Gomez-Aguilar, T. Cordova-Fraga, T. Abdeljawad, A. Khan, H. Khan, Analysis of fractal fractional malaria transmission model, Fractals 28 (2020) 2040041. [11] K. Jyotsna, A. Tandon, A mathematical model to study the impact of mining activities and pollution on forest resources and wildlife population, J. Biol. Syst. 25 (2017) 207–230. [12] S. Karthikeyan, P. Ramesh, M. Sambath, Stability analysis of fractional-order predator-prey model with anti-predator behaviour and prey refuge, J. Math. Model. 11(3) (2023) 527–546. [13] H. Khan, J. Alzabut, A. Shah, Z.Y. He, S. Etemad, S. Rezapour, A. Zada, On fractal-fractional wa terborne disease model: A study on theoretical and numerical aspects of solutions via simulations, Fractals 31 (2023) 2340055 [14] X. Liu, S. Ahmad, M. Rahman, Y. Nadeem, A.Akgul, Analysis of a TB and HIV co-infection model under Mittag-Leffler fractal-fractional derivative, Phys. Scr. 97 (2022) 054011. [15] N. Madani, Z. Hammouch, E. H. Azroul, New model of HIV/AIDS dynamics based on Caputo Fabrizio derivative order: Optimal strategies to control the spread, J. Comput. Sci. 90 (2025) 102612. [16] T. Mekkaoui, Z. Hammouch, Approximate analytical solutions to the Bagley-Torvik equation by the fractional iteration method, Ann. Univ. Craiova Math. Comput. Sci. Ser. 39 (2012) 251–256. [17] A.K. Misra, K. Lata, J.B. Shukla, A mathematical model for the depletion of forestry resources due to population and population pressure augmented industrialization, Int. J. Model. Simul. Sci. Comput. 5 (2014) 1350022. [18] I. Podlubny, Fractional Differential Equations: An Introduction to Fractional Derivatives, Ffrac tional Differential Equations, to Methods of their Solution and Some of their Applications, Elsevier, 1998. [19] M. Rahman, Generalized fractal–fractional order problems under non-singular Mittag-Leffler ker nel, Results Phys. 35 (2022) 105346. [20] K. Shah, M. Arfan, I. Mahariq, A. Ahmadian, S. Salahshour, M. Ferrara, Fractal-fractional mathe matical model addressing the situation of corona virus in Pakistan, Results Phys. 19 (2020) 103560. [21] J.B. Shukla, B. Dubey, Modelling the depletion and conservation of forestry resources: effects of population and pollution, J. Math. Biol. 36 (1997) 71–94. [22] J.B. Shukla, H.I. Freedman, V.M. Pal, O.P. Misra, M. Agarwal, A. Shukla, Degradation and subse quent regeneration of a forestry resource: a mathematical model, Ecol. Model. 44 (1989) 219–229. [23] A. Singh, S. Pippal, J. Sati, Atangana–Baleanu–Caputo (ABC), Caputo-Fabrizio (CF), and Caputo fractional derivative approaches in fuzzy time fractional cancer tumor growth models, J. Math. Model. 13(3) (2025) 685–706. [24] M.F. Uddin, M G. Hafez, Z. Hammouch, H. Rezazadeh, B. Baleanu, Traveling wave with beta derivative spatial-temporal evolution for describing the nonlinear directional couplers with meta materials via two distinct methods, Alex. Eng. J. 60 (2021) 1055–1065. [25] S.M. Ulam, A Collection of Mathematical Problems, Interscience Publishers, 1960. [26] S.M. Ulam, Problems in Modern Mathematics, Courier Corporation, 2004. [27] L. Verma, R. Meher, D.P. Pandya, Parameter estimation study of temporal fractional HIV/AIDS transmission model with fractal dimensions using real data in India, Math. Comput. Simul. 234 (2025) 135–150. [28] L. Verma, R. Meher, Study on generalized fuzzy fractional human liver model with Atangana Baleanu–Caputo fractional derivative, Eur. Phys. J. Plus 137 (2022) 1233 [29] L. Verma, R. Meher, O. Nikan, A.A. Al-Saedi, Numerical study on fractional order nonlinear SIR SI model for dengue fever epidemics, Sci. Rep. 15 (2022) 30677. [30] M.A.U.Waqih, N.A.Bhutto, N.H. Ghumro, S. Kumar, M.A. Salam, Rising environmental degrada tion and impact of foreign direct investment: an empirical evidence from SAARC region, J. Environ. Manag. 243 (2019) 472–480 | ||
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