Browsing by Author "Zeng, De-Qiang"

Now showing 1 - 2 of 2

FractionaI Impulsive Differential Equations: Exact Solutions, Integral Equations and Short Memory Case
(Walter De Gruyter GMBH, 2019) Baleanu, Dumitru; Zeng, De-Qiang; Baleanu, Dumitru; 56389
Fractional impulsive differential equations are revisited first. Some fundamental solutions of linear cases are given in this study. One straightforward technique without using integral equation is adopted to obtain exact solutions which are given by use of piecewise functions. Furthermore, a class of short memory fractional differential equations is proposed and the variable case is discussed. Mittag-Leffler solutions with impulses are derived which both satisfy the equations and impulsive conditions, respectively.
New variable-order fractional chaotic systems for fast image encryption
(Amer inst Physics, 2019) Wu, Guo-Cheng; Baleanu, Dumitru; Deng, Zhen-Guo; Baleanu, Dumitru; Zeng, De-Qiang; 56389
New variable-order fractional chaotic systems are proposed in this paper. A concept of short memory is introduced where the initial point in the Caputo derivative is varied. The fractional order is defined by the use of a piecewise constant function which leads to rich chaotic dynamics. The predictor-corrector method is adopted, and numerical solutions of fractional delay equations are obtained. Then, this concept is extended to fractional difference equations, and generalized chaotic behaviors are discussed numerically. Finally, the new fractional chaotic models are applied to block image encryption and each block has a different fractional order. The new chaotic system improves security of the image encryption and saves the encryption time greatly. Published under license by AIP Publishing.