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Tytuł artykułu

Stability analysis of conformable fractional-order nonlinear systems depending on a parameter

Identyfikatory
Warianty tytułu
Języki publikacji
EN
Abstrakty
EN
In this paper, the stability of conformable fractional-order nonlinear systems depending on a parameter is presented and described. Furthermore, The design of a feedback controller for the same class of conformable fractional-order systems is introduced. Illustrative examples are given at the end of the paper to show the effectiveness of the proposed results.
Wydawca
Rocznik
Strony
287--296
Opis fizyczny
Bibliogr. 23 poz., wykr.
Twórcy
autor
  • CEM Lab, Department of Electrical Engineering, National School of Engineering, University of Sfax, Sfax, Tunisia
autor
  • University of Guelma, Guelma, Algeria
autor
  • Department of Mathematics, College of Science, Jouf University, Aljouf, Saudi Arabia
  • Department of Mathematics, Faculty of Sciences of Sfax, Route Soukra, BP 1171, 3000 Sfax, Tunisia
  • Department of Mathematics, Faculty of Sciences of Sfax, University of Sfax, Route Soukra, BP 1171, 3000 Sfax, Tunisia
  • University of Badji Mokhtar, Annaba, Algeria
Bibliografia
  • [1] T. Abdeljawad, On conformable fractional calculus, J. Comput. Appl. Math. 279 (2015), 57-66.
  • [2] B. Ben Hamed, Z. Haj Salem and M. A. Hammami, Stability of nonlinear time-varying perturbed differential equations, Nonlinear Dynam. 73 (2013), no. 3, 1353-1365.
  • [3] A. Ben Makhlouf, M. A. Hammami and K. Sioud, Stability of fractional-order nonlinear systems depending on a parameter, Bull. Korean Math. Soc. 54 (2017), no. 4, 1309-1321.
  • [4] N. Engheta, On fractional calculus and fractional multipoles in electromagnetism, IEEE Trans. Antennas and Propagation 44 (1996), no. 4, 554-566.
  • [5] M. Eslami, Solitary wave solutions for perturbed nonlinear Schrodingers equation with Kerr law nonlinearity under the DAM, Optik 126 (2015), 1312-1317.
  • [6] B. Ghanmi, Stability of impulsive systems depending on a parameter, Math. Methods Appl. Sci. 39 (2016), no. 10, 2626-2646.
  • [7] H. A. Ghany, A. Hyder and M. Zakarya, Exact solutions of stochastic fractional Korteweg de-Vries equation with conformable derivatives, Chinese Phys. B 29 (2020), 1-15.
  • [8] S. He, K. Sun, K. Mei, B. Yan and S. Xu, Numerical analysis of a fractional-order chaotic system based on conformable fractional-order derivative, European Phys. J. Plus 36 (2017), 1-10.
  • [9] Y. Hong, Finite-time stabilization and stabilizability of a class of controllable systems, Systems Control Lett. 46 (2002), no. 4, 231-236.
  • [10] O. S. Iyiola, O. Tasbozan, A. Kurt and Y. Çenesiz, On the analytical solutions of the system of conformable time-fractional Robertson equations with 1-D diffusion, Chaos Solitons Fractals 94 (2017), 1-7.
  • [11] A. Jmal, M. Elloumi, O. Naifar, A. Ben Makhlouf and M. A. Hammami, State estimation for nonlinear conformable fractional-order systems: A healthy operating case and a faulty operating case, Asian J. Control 22 (2020), 1870-1879.
  • [12] R. Khalil, M. Al Horani, A. Yousef and M. Sababheh, A new definition of fractional derivative, J. Comput. Appl. Math. 264 (2014), 65-70.
  • [13] A. Korkmaz, Exact solutions to (3 + 1) conformable time fractional Jimbo-Miwa, Zakharov-Kuznetsov and modified Zakharov-Kuznetsov equations, Commun. Theor. Phys. (Beijing) 67 (2017), no. 5, 479-482.
  • [14] A. Korkmaz and K. Hosseini, Exact solutions of a nonlinear conformable time-fractional parabolic equation with exponential nonlinearity using reliable methods, Opt. Quantum Electron. 49 (2017), 1-10.
  • [15] N. Laskin, Fractional market dynamics, Phys. A 287 (2000), no. 3-4, 482-492.
  • [16] A. Oustaloup, La Dérivation Non Entière, théorie, synthèse et applications, Hermes, Paris, 1995.
  • [17] Q. Shen, D. Wang, S. Zhu and E. K. Poh, Finite-time fault-tolerant attitude stabilization for spacecraft with actuator saturation, IEEE Trans. Aerospace Electron. Syst. 451 (2015), 2390-2405.
  • [18] A. Souahi, O. Naifar, A. Ben Makhlouf and M. A. Hammami, Discussion on Barbalat lemma extensions for conformable fractional integrals, Internat. J. Control 92 (2019), no. 2, 234-241.
  • [19] H. Sun, A. Abdelwahad and B. Onaral, Linear approximation of transfer function with a pole of fractional order, IEEE Trans. Automat. Contr. 29 (1984), 441-444.
  • [20] O. Tasbozan, Y. Cenesiz and A. Kurt, New solutions for conformable fractional Boussinesq and combined KdV-mKdV equations using Jacobi elliptic function expansion method, European Phys. J. Plus 131 (2016), 1-10.
  • [21] I. Torres, J. C. Fabris and O. F. Piattella, Quantum cosmology of fab four John theory with conformable fractional derivative, Universe 6 (2020), DOI 10.3390/universe6040050.
  • [22] B. Xin, W. Peng and L. Guerrini, A continuous time Bertrand duopoly game with fractional delay and conformable derivative: Modeling, discretization process, Hopf bifurcation, and chaos, Front. Phys. 7 (2019), 84-93.
  • [23] A. Zavala-Río, I. Fantoni and G. Sanahuja, Finite-time observer-based output-feedback control for the global stabilisation of the PVTOL aircraft with bounded inputs, Internat. J. Systems Sci. 47 (2016), no. 7, 1543-1562.
Typ dokumentu
Bibliografia
Identyfikator YADDA
bwmeta1.element.baztech-248ac621-2679-40da-aa99-ca0eb1fcc7c5
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