Browsing by Author "Sun, HongGuang"

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Citation Count: Sun, HongGuang...et al. (2018). "A new collection of real world applications of fractional calculus in science and engineering", Communications in Nonlinear Science And Numerical Simulation, Vol. 64, pp. 213-231.
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
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 Count: Hajipour, Mojtaba...et al. (20199. "On an accurate discretization of a variable-order fractional reaction-diffusion equation", Communications in Nonlinear Science And Numerical Simulation, Vol. 69, pp. 119-133.
On an accurate discretization of a variable-order fractional reaction-diffusion equation
(Elsevier Science BV, 2019) Hajipour, Mojtaba; Jajarmi, Amin; Baleanu, Dumitru; Sun, HongGuang; 56389
The aim of this paper is to develop an accurate discretization technique to solve a class of variable-order fractional (VOF) reaction-diffusion problems. In the spatial direction, the problem is first discretized by using a compact finite difference operator. Then, a weighted-shifted Grunwald formula is applied for the temporal discretization of fractional derivatives. To solve the derived nonlinear discrete system, an accurate iterative algorithm is also formulated. The solvability, stability and L-2-convergence of the proposed scheme are derived for all variable-order alpha(t) is an element of (0, 1). The proposed method is of accuracy-order O(tau(3) + h(4)), where tau and h are temporal and spatial step sizes, respectively. Through some numerical simulations, the theoretical analysis and high-accuracy of the proposed method are verified. Comparative results also indicate that the accuracy of the new discretization technique is superior to the other methods available in the literature. Finally, the feasibility of the proposed VOF model is demonstrated by using the reported experimental data. (C) 2018 Elsevier B.V. All rights reserved.