Matematik Bölümü Yayın Koleksiyonu
Permanent URI for this collectionhttps://hdl.handle.net/20.500.12416/413
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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 - WoS: 64Citation - Scopus: 82Discrete Fractional Diffusion Equation(Springer, 2015) Baleanu, Dumitru; Zeng, Sheng-Da; Deng, Zhen-Guo; Wu, Guo-ChengThe tool of the discrete fractional calculus is introduced to discrete modeling of diffusion problem. A fractional time discretization diffusion model is presented in the Caputo-like delta's sense. The numerical formula is given in form of the equivalent summation. Then, the diffusion concentration is discussed for various fractional difference orders. The discrete fractional model is a fractionization of the classical difference equation and can be more suitable to depict the random or discrete phenomena compared with fractional partial differential equations.Article Citation - WoS: 146Citation - Scopus: 163Discrete Chaos in Fractional Delayed Logistic Maps(Springer, 2015) Baleanu, Dumitru; Wu, Guo-ChengRecently the discrete fractional calculus (DFC) started to gain much importance due to its applications to the mathematical modeling of realworld phenomena with memory effect. In this paper, the delayed logistic equation is discretized by utilizing the DFC approach and the related discrete chaos is reported. The Lyapunov exponent together with the discrete attractors and the bifurcation diagrams are given.