[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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