WoS İndeksli Yayınlar Koleksiyonu

Permanent URI for this collectionhttps://hdl.handle.net/20.500.12416/8653

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Author: search.filters.author.Wu, Guo-ChengLanguage: search.filters.language.en

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Now showing 1 - 10 of 42
  • Article
    Citation - WoS: 38
    Citation - Scopus: 40
    A New Application of the Fractional Logistic Map
    (Editura Acad Romane, 2016) Huang, Lan-Lan; Baleanu, Dumitru; Baleanu, Dumitru; Wu, Guo-Cheng; Zeng, Sheng-Da; Matematik
    The fractional chaotic map started to be applied in physics and engineering to properly treat some real-world phenomena. A shuffling method is proposed based on the fractional logistic map. The fractional difference order is used as a key. An image encryption scheme is designed by using the XOR operation and the security analysis is given. The obtained results demonstrate that the fractional difference order makes the encryption scheme highly secure.
  • Article
    Citation - WoS: 464
    Citation - Scopus: 528
    Discrete Fractional Logistic Map and Its Chaos
    (Springer, 2014) Baleanu, Dumitru; Wu, Guo-Cheng
    A discrete fractional logistic map is proposed in the left Caputo discrete delta's sense. The new model holds discrete memory. The bifurcation diagrams are given and the chaotic behaviors are numerically illustrated.
  • Article
    Citation - WoS: 51
    Citation - Scopus: 54
    Terminal Value Problems for the Nonlinear Systems of Fractional Differential Equations
    (Elsevier, 2021) Wu, Guo-Cheng; Baleanu, Dumitru; Shiri, Babak
    Terminal value problems of fractional nonlinear systems are studied in this paper. The existence and uniqueness are given. The regularity of the solution is obtained in the weighted spaces. Discretized piecewise polynomial collocation methods are proposed on the graded mesh. A convergence analysis and the order are presented. Numerical examples for supporting theoretical results and applications for population models are illustrated. (C) 2021 IMACS. Published by Elsevier B.V. All rights reserved.
  • Article
    Citation - WoS: 6
    Citation - Scopus: 7
    Reprint Of: Chaos Synchronization of the Discrete Fractional Logistic Map
    (Elsevier, 2015) Baleanu, Dumitru; Wu, Guo-Cheng
    In this paper, master slave synchronization for the fractional difference equation is studied with a nonlinear coupling method. The numerical simulation shows that the designed synchronization method can effectively synchronize the fractional logistic map. The Caputo-like delta derivative is adopted as the difference operator. (C) 2014 Elsevier B.V. All rights reserved.
  • Article
    Citation - WoS: 63
    Citation - Scopus: 70
    New Fractional Signal Smoothing Equations With Short Memory and Variable Order
    (Elsevier Gmbh, 2020) Shiri, Babak; Wu, Guo-Cheng; Baleanu, Dumitru; Ma, Chang-You
    In this paper, systems of fuzzy fractional differential equations with a lateral type of the Hukuhara derivative and the generalized Hukuhara derivative are numerically studied. Collocation method on discontinuous piecewise polynomial spaces is proposed. Convergence of the proposed method is analyzed. The superconvergent results on the graded mesh are studied. Examples are provided to support theoretical results. Finally, the effect of uncertainty in a diabetes model and its resulting complications is investigated as a practical application.
  • Article
    Citation - WoS: 67
    Citation - Scopus: 75
    Discrete Fractional Calculus for Interval-Valued Systems
    (Elsevier, 2021) Wu, Guo-Cheng; Baleanu, Dumitru; Wang, Hong-Yong; Huang, Lan-Lan
    This study investigates linear fractional difference equations with respect to interval-valued functions. Caputo and Riemann-Liouville differences are defined. w-monotonicity is introduced and discrete Leibniz integral laws are provided. Then exact solutions of two linear equations are obtained by Picard's iteration. In comparison with the deterministic initial problems, the solutions are given in discrete Mittag-Leffler functions with and without delay, respectively. This paper provides a novel tool to understand fractional uncertainty problems on discrete time domains. (C) 2020 Elsevier B.V. All rights reserved.
  • Article
    Citation - WoS: 95
    Citation - Scopus: 114
    Collocation Methods for Terminal Value Problems of Tempered Fractional Differential Equations
    (Elsevier, 2020) Wu, Guo-Cheng; Baleanu, Dumitru; Shiri, Babak
    A class of tempered fractional differential equations with terminal value problems are investigated in this paper. Discretized collocation methods on piecewise polynomials spaces are proposed for solving these equations. Regularity results are constructed on weighted spaces and convergence order is studied. Several examples are supported the theoretical parts and compared with other methods. (C) 2020 IMACS. Published by Elsevier B.V. All rights reserved.
  • Article
    Citation - WoS: 153
    Citation - Scopus: 162
    Chaos Synchronization of the Discrete Fractional Logistic Map
    (Elsevier, 2014) Baleanu, Dumitru; Wu, Guo-Cheng
    In this paper, master-slave synchronization for the fractional difference equation is studied with a nonlinear coupling method. The numerical simulation shows that the designed synchronization method can effectively synchronize the fractional logistic map. The Caputo-like delta derivative is adopted as the difference operator. (C) 2014 Elsevier B.V. All rights reserved.
  • Article
    Citation - WoS: 66
    Citation - Scopus: 75
    Some Further Results of the Laplace Transform for Variable-Order Fractional Difference Equations
    (Springernature, 2019) Wu, Guo-Cheng; Baleanu, Dumitru
    The Laplace transform is important for exact solutions of linear differential equations and frequency response analysis methods. In comparison with the continuous-time systems, less results can be available for fractional difference equations. This study provides some fundamental results of two kinds of fractional difference equations by use of the Laplace transform. Some discrete Mittag-Leffler functions are defined and their Laplace transforms are given. Furthermore, a class of variable-order and short memory linear fractional difference equations are proposed and the exact solutions are obtained.
  • Article
    Citation - WoS: 78
    Citation - Scopus: 88
    Spline Collocation Methods for Systems of Fuzzy Fractional Differential Equations
    (Pergamon-elsevier Science Ltd, 2020) Baleanu, Dumitru; Shiri, Babak; Wu, Guo-Cheng; Alijani, Zahra
    In this paper, systems of fuzzy fractional differential equations with a lateral type of the Hukuhara derivative and the generalized Hukuhara derivative are numerically studied. Collocation method on discontinuous piecewise polynomial spaces is proposed. Convergence of the proposed method is analyzed. The superconvergent results on the graded mesh are studied. Examples are provided to support theoretical results. Finally, the effect of uncertainty in a diabetes model and its resulting complications is investigated as a practical application. (C) 2019 Elsevier Ltd. All rights reserved.