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Application of Jumarie-Stancu collocation series method and multi-Step
Methodology: Sayed Saber 13. Saber S. Control of chaos in the Burke-Shaw
Formal analysis: Sayed Saber, Brahim Dridi system of fractal-fractional order in the sense
Writing–original draft: Abdullah Alahmari, of Caputo-Fabrizio. J Appl Math Comput Mech.
Mohammed Messaoudi 2024;23(1):83-96.
Writing–review & editing: All authors 14. Ahmed K, Adam H, Almutairi N, Saber S. Ana-
lytical solutions for a class of variable-order frac-
tional Liu system under time-dependent variable
coefficients. Results Phys. 2024;56:107311.
Availability of data 15. Almutairi N, Saber S. On chaos control of
nonlinear fractional Newton-Leipnik system via
Not applicable.
fractional Caputo-Fabrizio derivatives. Sci Rep.
2023;13:22726.
AI tools statement 16. Almutairi N, Saber S, and Ahmad H. The fractal-
fractional Atangana-Baleanu operator for pneu-
All authors confirm that no AI tools were used in monia disease: stability, statistical and numerical
the preparation of this manuscript. analyses. AIMS Math. 2023;8(12):29382-29410.
17. Almutairi N, Saber S. Chaos control and
numerical solution of time-varying fractional
References
Newton-Leipnik system using fractional
1. Zabidi NA, Majid ZA, Kilicman A, et al. Numer- Atangana-Baleanu derivatives. AIMS Math.
ical solution of fractional differential equations 2023;8(11):25863-25887.
with Caputo derivative by using numerical frac- 18. Petras I. Fractional-Order Nonlinear Systems:
tional predict–correct technique. Adv Cont Discr Modeling, Analysis and Simulation. Berlin:
Mod. 2022;2022:1-23. Springer; 2011.
2. Podlubny I. Fractional Differential Equations. 19. Ahmed KIA, Adam HDS, Almutairi N, et al. An-
San Diego: Academic Press; 1999. alytical solutions for a class of variable-order frac-
3. Arena P, Caponetto R, Fortuna L, and Porto M. tional Liu system under time-dependent variable
Nonlinear Noninteger Order Circuits and Systems coefficients. Results Phys. 2024;56:107311.
– An Introduction. Singapore: World Scientific; 20. Alhazmi M, Dawalbait F, Aljohani A, et al.
2000. Numerical approximation method and chaos for
4. Nisar KS, Farman M, Abdel-Aty, Ravichan- a chaotic system in sense of Caputo-Fabrizio
dran C. A review of fractional-order models operator. Thermal Sci. 2024;28(6B):5161-
for plant epidemiology. Prog Fract Differ Appl. 5168.
2024;10:489-521. 21. Almutairi N, Saber S. Chaos control and numer-
5. Ahmed E, Elgazzar AS. On fractional order dif- ical solution of time-varying fractional Newton-
ferential equations model for nonlocal epidemics. Leipnik system using fractional Atangana-
Physica A. 2007;379(2):607-614. Baleanu derivatives. AIMS Math. 2023;8:25863-
6. Li W, Wang Y, Cao J, Abdel-Aty M. Dynam- 25887.
ics and backward bifurcations of SEI tuberculosis 22. Alsulami A, Alharb RA, Albbogami TM, et al.
models in homogeneous and heterogeneous popu- Controlled chaos of a fractal–fractional Newton-
lations. J Math Anal Appl. 2025;543:128924. Leipnik system. Thermal Sci. 2024;28(6B).
7. Nisar KS, Farman M, Abdel-Aty M, Ravichan- 23. Alshehri MH, Saber S, and Duraihem FZ. Dy-
dran C. A review of fractional order epidemic namical analysis of fractional-order of IVGTT
models for life sciences problems: past, present glucose–insulin interaction. Int J Nonlin Sci Nu-
and future. Alexandria Eng J. 2024;95:283-305. mer Simul. 2023;24:1123-1140.
8. Bagley RL, Calico RA. Fractional order state 24. Alshehri MH, Duraihem FZ, Alalyani A, et al.
equations for the control of viscoelastically A caputo (discretization) fractional-order model
damped structures. J Guid Control Dyn. 1991; of glucose-insulin interaction: numerical solu-
14:304-311. tion and comparisons with experimental data. J
9. Heaviside O. Electromagnetic Theory. New York: Taibah Univ Sci. 2021;15:26-36.
Chelsea Publishing Company; 1971. 25. Sayed Saber, Eihab Bashier, Alzahrani S., Noa-
10. Kusnezov D, Bulgac A, Dang GD. Quantum L´evy man IA. A mathematical model of glucose-insulin
processes and fractional kinetics. Phys Rev Lett. interaction with time delay. J. Appl Comput
1999;82:1136-1139. Math. 2018;7(3):1-5.
11. Almutairi N, Saber S. Existence of chaos and the 26. Ahmed KIA, Adam HDS, Yousiff MY, et al.
approximate solution of the Lorenz–L¨u–Chen sys- Different strategies for diabetes by mathemati-
tem with the Caputo fractional operator. AIP cal modeling: applications of fractal-fractional
Adv. 2024;14:015112. derivatives in the sense of Atangana-Baleanu. Re-
12. Hilfer R. Applications of Fractional Calculus in sults Phys. 2023;26: 106892.
Physics. Singapore: World Scientific; 2000:87- 27. Ahmed KIA, Adam HDS, Yousiff MY, et al. Dif-
130. ferent strategies for diabetes by mathematical
479