Browsing by Author "Zhang, Yong"

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Citation - WoS: 1286
Citation - Scopus: 1420
A new collection of real world applications of fractional calculus in science and engineering
(Elsevier, 2018) Sun, HongGuang; Zhang, Yong; Baleanu, Dumitru; Chen, Wen; Chen, YangQuan; 56389; Matematik
Fractional calculus is at this stage an arena where many models are still to be introduced, discussed and applied to real world applications in many branches of science and engineering where nonlocality plays a crucial role. Although researchers have already reported many excellent results in several seminal monographs and review articles, there are still a large number of non-local phenomena unexplored and waiting to be discovered. Therefore, year by year, we can discover new aspects of the fractional modeling and applications. This review article aims to present some short summaries written by distinguished researchers in the field of fractional calculus. We believe this incomplete, but important, information will guide young researchers and help newcomers to see some of the main real-world applications and gain an understanding of this powerful mathematical tool. We expect this collection will also benefit our community. (C) 2018 Elsevier B.V. All rights reserved.
Citation - WoS: 55
Citation - Scopus: 63
Relaxation and diffusion models with non-singular kernels
(Elsevier Science Bv, 2017) Sun, HongGuang; Hao, Xiaoxiao; Zhang, Yong; Baleanu, Dumitru; Matematik
Anomalous relaxation and diffusion processes have been widely quantified by fractional derivative models, where the definition of the fractional-order derivative remains a historical debate due to its limitation in describing different kinds of non-exponential decays (e.g. stretched exponential decay). Meanwhile, many efforts by mathematicians and engineers have been made to overcome the singularity of power function kernel in its definition. This study first explores physical properties, of relaxation and diffusion models where the temporal derivative was defined recently using an exponential kernel. Analytical analysis shows that the Caputo type derivative model with an exponential kernel cannot characterize non-exponential dynamics well-documented in anomalous relaxation and diffusion. A legitimate extension of the previous derivative is then proposed by replacing the exponential kernel with a stretched" exponential kernel. Numerical tests show that the Caputo type derivative model with the stretched exponential kernel can describe a much wider range of anomalous diffusion than the exponential kernel, implying the potential applicability of the new derivative in quantifying real-world, anomalous relaxation and diffusion processes. (C) 2016 Elsevier B.V. All rights reserved.