×
Koca, Ilknur; Atangana, Abdon

Some chaotic mathematical models with stochastic resetting. (English) Zbl 1515.34020

Fractals 30, No. 8, Article ID 2240212, 23 p. (2022).

MSC:

34A08 Fractional ordinary differential equations
34A34 Nonlinear ordinary differential equations and systems
34C28 Complex behavior and chaotic systems of ordinary differential equations
34F05 Ordinary differential equations and systems with randomness
65L05 Numerical methods for initial value problems involving ordinary differential equations

Keywords:

stochastic chaotic models; fractional differential operators; new number; Lagrange polynomial interpolation

Software:

DFOC; sysdfod
Cite Review PDF
Full Text: DOI

References:

[1] Sweilam, N. H., AL-Mekhlafi, S. M. and Mohamed, D. G., Novel chaotic systems with fractional differential operators: Numerical approaches, Chaos Solitons Fractals142 (2021) 110475. · Zbl 1496.65094
[2] Atangana, A., Extension of rate of change concept: From local to nonlocal operators with applications, Results Phys.19 (2020) 103515.
[3] Khan, M. A., Ismail, M., Ullah, S. and Farhan, M., Fractional order SIR model with generalized incidence rate, AIMS Math.5(3) (2020) 1856. · Zbl 1484.92117
[4] Akçetin, E., Koca, I. and Kiliç, M. B., New analysis and application of fractional order Schrödinger equation using with Atangana-Batogna numerical scheme, Numer. Methods Partial Differential Equations37 (2020) 196-209. · Zbl 1535.65120
[5] Choi, S. C. and Ki, M., Estimating the reproductive number and the outbreak size of novel coronavirus disease (Covid-19) using mathematical model in republic of Korea, Epidemiol. Health42 (2020) 10.
[6] Lin, Q., Zhao, S., Gao, D., Lou, Y., Yang, S., Musa, S. S., Wang, M. H., Cai, Y., Wang, W., Yang, L. and He, D., A conceptual model for the coronavirus disease 2019 (Covid-19) outbreak in Wuhan, China with individual reaction and governmental action, Int. J. Infect. Dis.93 (2020) 211-216.
[7] Petras, I., Fractional-Order Nonlinear Systems Modeling, Analysis and Simulation (Springer, 2011). · Zbl 1228.34002
[8] Sambas, A., Vaidyanathan, S., Tlelo-Cuautle, E., Zhang, S., Guillen-Fernandez, O., Sukono, Hidayat, Y. and Gundara, G., A novel chaotic system with two circles of equilibrium points: Multistability, electronic circuit and FPGA realization, Electronics8(11) (2019) 1211.
[9] Ramanathan, C., Abishek Arun, R., Sriharsha, K. V., Hamsavaahini, S., Abirami, R., Saranya, J. N., Subhathira, R., Kalaiselvan, K. and Raajan, N. R., A new chaotic attractor from Rucklidge system and its application in secured communication using OFDM, in 11th International Conference on Intelligent Systems and Control, 2017.
[10] Lü, J., Chen, G. and Cheng, D., A new chaotic system and beyond: The generalized Lorenz-like system, Internat. J. Bifur. Chaos14(5) (2004) 1507-1537. · Zbl 1129.37323
[11] Alzaid, S. S., Alkahtani, B. S. T., Sharma, S. and Dubey, R. S., Numerical solution of fractional model of HIV-1 infection in framework of different fractional derivatives, J. Funct. Spaces2021 (2021) 6642957, https://doi.org/10.1155/2021/6642957. · Zbl 1469.92004
[12] Almuqrin, M. A., Goswami, P., Sharma, S., Khan, I., Dubey, R. S. and Khan, A., Fractional model of Ebola virus in population of bats in frame of Atangana-Baleanu fractional derivative, Results Phys.26 (2021) 104295.
[13] Malyk, I., Mohammed, M., Shrahili, A., Shafay, A. R., Goswami, P., Sharma, S. and Dubey, R. S., Analytical solution of non-linear fractional Burger’s equation in the framework of different fractional derivative operators, Results Phys.19 (2020) 103397.
[14] Atangana, A. and Araz, S. Igret, New concept in calculus: Piecewise differential and integral operators, Chaos Solitons Fractals145 (2021) 110638. · Zbl 1470.65125
[15] Atangana, A. and Baleanu, D., New fractional derivatives with non-local and non-singular kernel: Theory and application to heat transfer model, Therm. Sci.20(2) (2016) 763-769.
[16] Caputo, M. and Fabrizio, M., A new definition of fractional derivative without singular kernel, Prog. Fract. Differ. Appl.1(2) (2015) 73-85.
[17] Podlubny, I., Fractional Differential Equations (Academic Press, New York, 1999). · Zbl 0924.34008
[18] Toufik, M. and Atangana, A., New numerical approximation of fractional derivative with non-local and non-singular kernel: Application to chaotic models, Eur. Phys. J. Plus132(10) (2017) 444.
This reference list is based on information provided by the publisher or from digital mathematics libraries. Its items are heuristically matched to zbMATH identifiers and may contain data conversion errors. In some cases that data have been complemented/enhanced by data from zbMATH Open. This attempts to reflect the references listed in the original paper as accurately as possible without claiming completeness or a perfect matching.