Matematik Bölümü Yayın Koleksiyonu
Permanent URI for this collectionhttps://hdl.handle.net/20.500.12416/413
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Article Citation - WoS: 38Citation - Scopus: 40A New Application of the Fractional Logistic Map(Editura Acad Romane, 2016) Huang, Lan-Lan; Baleanu, Dumitru; Baleanu, Dumitru; Wu, Guo-Cheng; Zeng, Sheng-Da; MatematikThe 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.Letter Citation - WoS: 46Citation - Scopus: 47Discrete Fractional Watermark Technique(Zhejiang Univ, 2020) Shiri, Babak; Baleanu, Dumitru; Wang, Zai-rongThe fractional logistic map holds rich dynamics and is adopted to generate chaotic series. A watermark image is then encrypted and inserted into the original images. Since the encryption image takes the fractional order within (0, 1], it increases the key space and becomes difficult to attack. This study provides a robust watermark method in the protection of the copyright of hardware, images, and other electronic files.Article Citation - WoS: 464Citation - Scopus: 528Discrete Fractional Logistic Map and Its Chaos(Springer, 2014) Baleanu, Dumitru; Wu, Guo-ChengA 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 - Scopus: 14Several Fractional Differences and Their Applications To Discrete Maps(L and H Scientific Publishing, LLC, 2015) Baleanu, D.; Zeng, S.-D.; Wu, G.-C.Several definitions of fractional differences are discussed. Their applications to fractional maps are compared. As an example, the logistic equation of integer order is discretized by these fractional difference methods. The comparative results show that the discrete fractional calculus is an efficient tool and the maps derived in this way have simpler forms but hold rich dynamical behaviors. © 2015 L & H Scientific Publishing, LLC.Article Citation - WoS: 6Citation - Scopus: 7Reprint Of: Chaos Synchronization of the Discrete Fractional Logistic Map(Elsevier, 2015) Baleanu, Dumitru; Wu, Guo-ChengIn 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: 22Citation - Scopus: 21Novel Aspects of Discrete Dynamical Type Inequalities Within Fractional Operators Having Generalized (h)over-Bar Mittag-Leffler Kernels and Application(Pergamon-elsevier Science Ltd, 2021) Sultana, Sobia; Hammouch, Zakia; Jarad, Fahd; Hamed, Y. S.; Rashid, SaimaDiscrete fractional calculus (DFC) has had significant advances in the last few decades, being successfully employed in the time scale domain (h) over barZ. Understanding of DFC has demonstrated a valuable improvement in neural networks and modeling in other terrains. In the context of Riemann form (ABTL), we discuss the discrete fractional operator influencing discrete Atangana-Baleanu (AB)-fractional operator having (h) over bar -discrete generalized Mittag-Leffler kernels. In the approach being presented, some new Polya-Szego and Chebyshev type inequalities introduced within discrete AB-fractional operators having h-discrete generalized Mittag-Leffler kernels. By analyzing discrete AB-fractional operators in the time scale domain Z, we can perform a comparison basis for notable outcomes derived from the aforesaid operators. This type of discretization generates novel outcomes for synchronous functions. The specification of this proposed strategy simply demonstrates its efficiency, precision, and accessibility in terms of the methodology of qualitative approach of discrete fractional difference equation solutions, including its stability, consistency, and continual reliance on the initial value for the solutions of many fractional difference equation initial value problems. The repercussions of the discrete AB-fractional operators can depict new presentations for various particular cases. Finally, applications concerning bounding mappings are also illustrated. (C) 2021 Elsevier Ltd. All rights reserved.Book Part Citation - Scopus: 15Discrete Fractional Masks and Their Applications To Image Enhancement(De Gruyter, 2019) Baleanu, D.; Bai, Y.-R.; Wu, G.-C.Fractional differences for image enhancement are revisited and the general methodology is illustrated in this chapter. Several fractional differences are theoretically analyzed and numerically compared. The weight coefficients derived from the discrete fractional calculus are a set of conserved quantities and they are suitable for image processing. Then a discrete fractional mask is designed within the Caputo difference and the mask coefficients are given by use of the Gamma functions. In comparison with the Grünwald-Letnikov difference and Riemann-Liouville masks, the results show this novel mask’s efficiency and simplicity. © 2019 Walter de Gruyter GmbH, Berlin/Boston.Article Citation - WoS: 67Citation - Scopus: 75Discrete Fractional Calculus for Interval-Valued Systems(Elsevier, 2021) Wu, Guo-Cheng; Baleanu, Dumitru; Wang, Hong-Yong; Huang, Lan-LanThis 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: 153Citation - Scopus: 162Chaos Synchronization of the Discrete Fractional Logistic Map(Elsevier, 2014) Baleanu, Dumitru; Wu, Guo-ChengIn 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.Letter Discrete fractional watermark technique(Zhejiang Univ, 2020) Wang, Zai-rong; Shiri, Babak; Baleanu, DumitruThe fractional logistic map holds rich dynamics and is adopted to generate chaotic series. A watermark image is then encrypted and inserted into the original images. Since the encryption image takes the fractional order within (0, 1], it increases the key space and becomes difficult to attack. This study provides a robust watermark method in the protection of the copyright of hardware, images, and other electronic files.