Browsing by Author "Tang, Yifa"

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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. (2017). Effects of HIV infection on CD4(+) T-cell population based on a fractional-order model, Advances in Difference Equations.
Effects of HIV infection on CD4(+) T-cell population based on a fractional-order model
(Springer Open, 2017) Arshad, Sadia; Baleanu, Dumitru; Bu, Weiping; Tang, Yifa; 56389
In this paper, we study the HIV infection model based on fractional derivative with particular focus on the degree of T-cell depletion that can be caused by viral cytopathicity. The arbitrary order of the fractional derivatives gives an additional degree of freedom to fit more realistic levels of CD4(+) cell depletion seen in many AIDS patients. We propose an implicit numerical scheme for the fractional-order HIV model using a finite difference approximation of the Caputo derivative. The fractional system has two equilibrium points, namely the uninfected equilibrium point and the infected equilibrium point. We investigate the stability of both equilibrium points. Further we examine the dynamical behavior of the system by finding a bifurcation point based on the viral death rate and the number of new virions produced by infected CD4(+) T-cells to investigate the influence of the fractional derivative on the HIV dynamics. Finally numerical simulations are carried out 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.
Citation Count: Arshad, Sadiaa; Baleanu, Dumitru; Tang, Yifa (2019). "Fractional differential equations with bio-medical applications", Applications in Engineering, Life and Social Sciences, Part A, pp. 1-20.
Fractional differential equations with bio-medical applications
(2019) Arshad, Sadiaa; Baleanu, Dumitru; Tang, Yifa; 56389
In this chapter, we investigate the dynamics of fractional order models in bio-medical. First, we examine the fractional order model of HIV Infection and analyze the stability results for non-infected and infected equilibrium points. Then, we concentrate on the fractional order tumor growth model and establish a sufficient condition for existence and uniqueness of the solution of the fractional order tumor growth model. Local stability of the four equilibrium points of the model, namely the tumor free equilibrium, the dead equilibrium of type 1, the dead equilibrium of type 2 and the coexisting equilibrium is investigated by applying Matignons condition. Dynamics of the fractional order tumor model is numerically investigated by varying the fractional-order parameter and the system parameters. © 2019 Walter de Gruyter GmbH, Berlin/Boston.
Citation Count: Arshad, Sadia...et al. (2021). "Simpson's method for fractional differential equations with a non-singular kernel applied to a chaotic tumor model", PHYSICA SCRIPTA, Vol. 96, No. 12.
Simpson's method for fractional differential equations with a non-singular kernel applied to a chaotic tumor model
(2021) Arshad, Sadia; Saleem, Iram; Defterli, Özlem; Tang, Yifa; Baleanu, Dumitru; 56389
This manuscript is devoted to describing a novel numerical scheme to solve differential equations of fractional order with a non-singular kernel namely, Caputo-Fabrizio. First, we have transformed the fractional order differential equation to the corresponding integral equation, then the fractional integral equation is approximated by using the Simpson's quadrature 3/8 rule. The stability of the proposed numerical scheme and its convergence is analyzed. Further, a cancer growth Caputo-Fabrizio model is solved using the newly proposed numerical method. Moreover, the numerical results are provided for different values of the fractional-order within some special cases of model parameters.
Citation Count: Arshad, Sadia...et al. (2020). "THE ROLE OF OBESITY IN FRACTIONAL ORDER TUMOR-IMMUNE MODEL", University Politehnica of Bucharest Scientific Bulletin-Series A-Applied Mathematics and Physics, Vol. 82, no. 2, pp. 181-196.
THE ROLE OF OBESITY IN FRACTIONAL ORDER TUMOR-IMMUNE MODEL
(2020) Arshad, Sadia; Yildiz, Tugba Akman; Baleanu, Dumitru; Tang, Yifa; 56389
This work investigates the tumor-obesity model via a fractional operator to analyze the interactions between cancer and obesity, since fractional derivatives capture the long formation of cancerous tumor cells that might takes years to develop. It is known that fat cells enhance the development of cancerous tumor cells. To examine how the immune system is influenced due to fat cells, interactions of four types of cell population, namely tumor cells, immune cells, normal cells and fat cells are examined. We investigate the equilibrium points and discuss their stability analytically. Numerical simulations are carried out to verify the analytical results, demonstrating that a low fat diet results in a smaller tumor burden as compared to a high-caloric diet.