Browsing by Author "Huang, Jianfei"

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Citation Count: Arshad, Sadia...et al. (2018). "A Fourth Order Finite Difference Method for Time-Space Fractional Diffusion Equations", East Asian Journal on Applied Mathematics, Vol. 8, No. 4, pp. 764-781.
A Fourth Order Finite Difference Method for Time-Space Fractional Diffusion Equations
(Global Science Press, 2018) Arshad, Sadia; Baleanu, Dumitru; Huang, Jianfei; Tang, Yifa; Zhao, Yue; 56389
A finite difference method for a class of time-space fractional diffusion equations is considered. The trapezoidal formula and a fourth-order fractional compact difference scheme are, respectively, used in temporal and spatial discretisations and the method stability is studied. Theoretical estimates of the convergence in the L-2 -norm are shown to be O(tau(2) + h(4)), where tau and h are time and space mesh sizes. Numerical examples confirm theoretical results.
Citation Count: Arshad, S...et al. (2016). Dynamical analysis of fractional order model of immunogenic tumors. Advance In Mechanical Engineering, 8(7). http://dx.doi.org/10.1177/1687814016656704
Dynamical analysis of fractional order model of immunogenic tumors
(Sage Publications Ltd, 2016) Arshad, Sadia; Baleanu, Dumitru; Huang, Jianfei; Tang, Yifa; Al Qurashi, Maysaa Mohamed
In this article, we examine the fractional order model of the cytotoxic T lymphocyte response to a growing tumor cell population. We investigate the long-term behavior of tumor growth and explore the conditions of tumor elimination analytically. We establish the conditions for the tumor-free equilibrium and tumor-infection equilibrium to be asymptotically stable and provide the expression of the basic reproduction number. Existence of physical significant tumor-infection equilibrium points is investigated analytically. We show that tumor growth rate, source rate of immune cells, and death rate of immune cells play vital role in tumor dynamics and system undergoes saddle-node and transcritical bifurcation based on these parameters. Furthermore, the effect of cancer treatment is discussed by varying the values of relevant parameters. Numerical simulations are presented to illustrate the analytical results.
Citation Count: Arshad, Sadia...et al. (2018). Finite Difference Method for Time-Space Fractional Advection-Diffusion Equations with Riesz Derivative, Entropy, 20(5).
Finite Difference Method for Time-Space Fractional Advection-Diffusion Equations with Riesz Derivative
(MDPI, 2018) Arshad, Sadia; Baleanu, Dumitru; Huang, Jianfei; Al Qurashi, Maysaa Mohamed; Tang, Yifa; Zhao, Yue; 56389
In this article, a numerical scheme is formulated and analysed to solve the time-space fractional advection-diffusion equation, where the Riesz derivative and the Caputo derivative are considered in spatial and temporal directions, respectively. The Riesz space derivative is approximated by the second-order fractional weighted and shifted Grunwald-Letnikov formula. Based on the equivalence between the fractional differential equation and the integral equation, we have transformed the fractional differential equation into an equivalent integral equation. Then, the integral is approximated by the trapezoidal formula. Further, the stability and convergence analysis are discussed rigorously. The resulting scheme is formally proved with the second order accuracy both in space and time. Numerical experiments are also presented to verify the theoretical analysis.