SavedAdd your journal

Journals / An International Journal of Optimization and Control: Theories & Applications (IJOCTA) / 2022 / Cilt: 12 - Sayı: 1

Theory and applications of new fractional-order chaotic system under Caputo operator

Ndolane Sene
Pages
20–28
Publication Date
2022-10-11
DOI
—
🏛️Bibliographic metadata and full text access for this article are provided via DergiPark.
DergiPark Record ↗
✨

AI Summary & Key Takeaways

AI Insight
⚡ TL;DR(Too Long; Didn't Read)

The presence of coexisting attractors for partic- ular values of the parameters of the presented fractional-order chaotic model has been studied

📌 3 Key Takeaways

🎯
Objective & Hypothesis:This paper introduces the properties of a fractional-order chaotic system de- scribed by the Caputo derivative.
📊
Key Findings & Data:The impact of the fractional-order derivative has been focused on.
💡
Conclusion & Impact:The presence of coexisting attractors for partic- ular values of the parameters of the presented fractional-order chaotic model has been studied
🔬Design:Modeling & Simulation
📍Scope:Comprehensive Sample
⚙️Variables:Domain Parameters

Abstract

This paper introduces the properties of a fractional-order chaotic system de- scribed by the Caputo derivative. The impact of the fractional-order derivative has been focused on. The phase portraits in different orders are obtained with the aids of the proposed numerical discretization, including the discretization of the Riemann-Liouville fractional integral. The stability analysis has been used to help us to delimit the chaotic region. In other words, the region where the order of the Caputo derivative involves and where the presented system in this paper is chaotic. The nature of the chaos has been established using the Lyapunov exponents in the fractional context. The schematic circuit of the proposed fractional-order chaotic system has been presented and simulated in via Mutltisim. The results obtained via Multisim simulation of the chaotic circuit are in good agreement with the results with Matlab simulations. That provided the fractional operators can be applied in real- worlds applications as modeling electrical circuits. The presence of coexisting attractors for partic- ular values of the parameters of the presented fractional-order chaotic model has been studied

🔖

Cite This Article

Sene, N. (2022). Theory and applications of new fractional-order chaotic system under Caputo operator. An International Journal of Optimization and Control: Theories & Applications (IJOCTA), Cilt: 12 - Sayı: 1, 20–28. https://ajindex.com/articles/440524

📄 Full Text PDF Viewer

📄

PDF görüntüleyici hazırlanıyor...

References (3)

  1. 1] Kilbas, A. A., Srivastava, H. M., & Trujillo, J. J. (2006). Theory and applications of frac- tional differential equations. Vol. 204. Else- vier. [2] Yavuz, M. (2019). Characterizations of two different fractional operators without singu- lar kernel. Mathematical Modelling of Natural Phenomena, 14(3), 302. [3] Khan, A., Li, Y., Shah, K., & Khan, T. S. (2017). On coupled-laplacian fractional dif- ferential equations with nonlinear boundary conditions. Complexity, p.9. [4] Zafar, Z. U. A., Sene, N., Rezazadeh, H., & Esfandian, N. (2021). Tangent nonlinear equation in context of fractal fractional oper- ators with nonsingular kernel. Mathematical Sciences, 1-11. [5] Sene, N. (2020). Second-grade fluid model with Caputo–Liouville generalized fractional derivative. Chaos, Solitons & Fractals, 133, 109631. [6] Mansal, F., & Sene, N. (2020). Analysis of fractional fishery model with reserve area in the context of time-fractional order deriva- tive. Chaos, Solitons & Fractals, 140, 110200. [7] Jarad, F., Abdeljawad, T., & Baleanu, D. (2017). On the generalized fractional deriva- tives and their Caputo modification. J. Non- linear Sci. Appl., 10, 2607-2619. [8] Podlubny, I. (1999).
  2. Fractional Differential Equations, Mathematics in Science and En- gineering, Academic Press,
  3. New York, NY, USA, 198. [9] P ́erez, J. E. S., G ́omez-Aguilar, J. F., Baleanu, D., & Tchier, F. (2018). Chaotic at- tractors with fractional conformable deriva- tives in the Liouville–Caputo sense and its dynamical behaviors. Entropy, 20(5), 384. [10] G ́omez-Aguilar, J. F., Abro, K. A., Kolebaje, O., & Yildirim, A. (2019). Chaos in a cal- cium oscillation model via Atangana-Baleanu operator with strong memory. The European Physical Journal Plus, 134(4), 1-9. [11] Sene, N. (2021). Introduction to the fractional-order chaotic system under frac- tional operator in Caputo sense. Alexandria Engineering Journal, 60(4), 3997-4014. [12] Akgul, A. (2019). Chaotic oscillator based on fractional order memcapacitor. Journal of Circuits, Systems and Computers, 28(14), 1950239. [13] Munoz-Pacheco, J. M., Zambrano-Serrano, E., Volos, C., Jafari, S., Kengne, J., & Rajagopal, K. (2018). A new fractional- order chaotic system with different families of hidden and self-excited attractors. Entropy, 20(8), 564. [14] Sene, N. (2020). Analysis of a four- dimensional hyperchaotic system described by the Caputo–Liouville fractional derivative. Complexity, 2020. [15] Khan, A., G ́omez-Aguilar, J. F., Abdel- jawad, T.