Browsing by Author "Huang, Lan-Lan"

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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; 56389
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.
Discrete fractional calculus for interval-valued systems
(Elsevier, 2021) Huang, Lan-Lan; Baleanu, Dumitru; Wu, Guo-Cheng; Baleanu, Dumitru; Wang, Hong-Yong; 56389
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.
Fractional discrete-time diffusion equation with uncertainty: Applications of fuzzy discrete fractional calculus
(Elsevier Science Bv, 2018) Huang, Lan-Lan; Baleanu, Dumitru; Baleanu, Dumitru; Mo, Zhi-Wen; Wu, Guo-Cheng; 56389
This study provides some basics of fuzzy discrete fractional calculus as well as applications to fuzzy fractional discrete-time equations. With theories of r-cut set, fuzzy Caputo and Riemann-Liouville fractional differences are defined on a isolated time scale. Discrete Leibniz integral law is given by use of w-monotonicity conditions. Furthermore, equivalent fractional sum equations are established. Fuzzy discrete Mittag-Leffler functions are obtained by the Picard approximation. Finally, fractional discrete-time diffusion equations with uncertainty is investigated and exact solutions are expressed in form of two kinds of fuzzy discrete Mittag-Leffler functions. This paper suggests a discrete time tool for modeling discrete fractional systems with uncertainty. (C) 2018 Elsevier B.V. All rights reserved.
Novel Mittag-Leffler Stability of Linear Fractional Delay Difference Equations With İmpulse
(Pergamon-elsevier Science Ltd, 2018) Wu, Guo-Cheng; Baleanu, Dumitru; Baleanu, Dumitru; Huang, Lan-Lan; 56389
In this letter we propose a class of linear fractional difference equations with discrete time delay and impulse effects. The exact solutions are obtained by use of a discrete Mittag-Leffler function with delay and impulse. Besides, we provide comparison principle, stability results and numerical illustration. (C) 2018 Elsevier Ltd. All rights reserved.
Numerical solutions of interval-valued fractional nonlinear differential equations
(Springer Heidelberg, 2019) Huang, Lan-Lan; Baleanu, Dumitru; Liu, Bao-Qing; Baleanu, Dumitru; Wu, Guo-Cheng; 56389
.A class of interval-valued fractional nonlinear differential equations is proposed in this paper. The system is reduced to two kinds of standard fractional differential equations if w -monotone conditions are provided. Furthermore, two classes of fractional integral equations are obtained and the predictor-corrector method is used for numerical solutions.