The DOI matches its Crossref record; 8 of the 8 references it cites were found in a registry or an index.
Modeling attractors of chaotic dynamical systems with fractal–fractional operators
Abstract
Abstract In this paper, newly proposed differential and integral operators called the fractal–fractional derivatives and integrals have been used to predict chaotic behavior of some attractors from applied mathematics. These new differential operators are convolution of fractal derivative with power law, exponential decay law with Delta-Dirac property and the generalized Mittag-Leffler function with Delta-Dirac property, respectively. These new operators will be able to capture self-similarities in the chaotic attractors under investigation. We presented, in general, three numerical schemes that can be used to solve such systems of nonlinear differential equations. The general conditions for the existence and the uniqueness of the exact solutions are obtained. These new differential and integral operators applied in five selected chaotic attractors with numerical simulations for varying values of fractional order α and the fractal dimension τ have yielded very interesting results. It is to be believed that this research study will open new doors for in-depth investigation in dynamical systems of varying nature.
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Cites
CHEN, G., & UETA, T. (1999) · International Journal of Bifurcation and Chaos · doi:10.1142/s0218127499001024 · Cited by 2,838
A chaotic attractor from Chua's circuit
Matsumoto, T. (1984) · IEEE Transactions on Circuits and Systems · doi:10.1109/tcs.1984.1085459 · Cited by 746
Localization of hidden Chuaʼs attractors
Leonov, G. A., Kuznetsov, N. V., & Vagaitsev, V. I. (2011) · Physics Letters A · doi:10.1016/j.physleta.2011.04.037 · Cited by 710
GENERATING MULTISCROLL CHAOTIC ATTRACTORS: THEORIES, METHODS AND APPLICATIONS
Lü, J., & Chen, G. (2006) · International Journal of Bifurcation and Chaos · doi:10.1142/s0218127406015179 · Cited by 547
Anomalous diffusion modeling by fractal and fractional derivatives
Chen, W., Sun, H., Zhang, X., & Korošak, D. (2010) · Computers & Mathematics with Applications · doi:10.1016/j.camwa.2009.08.020 · Cited by 521
Arqub, O. A. (2018) · International Journal of Numerical Methods for Heat & Fluid Flow · doi:10.1108/hff-07-2016-0278 · Cited by 251
Fractional modeling of blood ethanol concentration system with real data application
Qureshi, S., Yusuf, A., Shaikh, A. A., Inc, M., & Baleanu, D. (2019) · Chaos: An Interdisciplinary Journal of Nonlinear Science · doi:10.1063/1.5082907 · Cited by 199
Self-citation(1996) · Analog Integrated Circuits and Signal Processing · doi:10.1007/bf00166419 · Cited by 92
Metadata
- Authors
- Atangana, A., & Qureshi, S.
- Venue
- Chaos, Solitons & Fractals
- Publisher
- Elsevier BV
- Published
- 2019-06
- Volume
- 123
- Pages
- 320-337
- ISSN
- 0960-0779 (ISSN-L)
- OpenAlex
- W2938708012
- Cited by
- 420
- References
- 8
- FWCI
- 29.73
- Type
- journal article
- Language
- en
- Open access
- closed
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- Atangana, A., & Qureshi, S. (2019). Modeling attractors of chaotic dynamical systems with fractal–fractional operators. Chaos, Solitons & Fractals. https://doi.org/10.1016/j.chaos.2019.04.020
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Contains information from the Semantic Scholar Academic Graph Datasets, made available under the ODC Attribution License (ODC-BY 1.0).
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