WoS İndeksli Yayınlar Koleksiyonu
Permanent URI for this collectionhttps://hdl.handle.net/20.500.12416/8653
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Article Citation - WoS: 11Numerical and Bifurcations Analysis for Multi Order Fractional Model of Hiv Infection of Cd4+t-cells(Univ Politehnica Bucharest, Sci Bull, 2016) Alipour, Mohsen; Baleanu, Dumitru; Arshad, Sadia; Baleanu, Dumitru; MatematikIn this paper, we solve the dynamical system of HIV infection of CD4(+) T cells within the multi-order fractional derivatives. The Bernstein operational matrices in arbitrary interval [a,b] are applied to obtain the approximate analytical solution of the model. In this way, the fractional differential equations are reduced to an algebraic easily solvable system. The obtained solutions are accurate and the method is very efficient and simple in implementation. With the help of bifurcation analysis, we acquired the critical value of viral death rate, that is, if viral death rate is greater than the critical value then level of virus particles starts to decline and thus free virus will eventually eliminate and patient is cured. Further, we found the threshold for viral infection rate analytically, which assures the stability of uninfected equilibrium and virus will ultimately eradicate.Article Citation - WoS: 6Citation - Scopus: 8The Role of Obesity in Fractional Order Tumor-Immune Model(Univ Politehnica Bucharest, Sci Bull, 2020) Arshad, Sadia; Baleanu, Dumitru; Yildiz, Tugba Akman; Baleanu, Dumitru; Tang, Yifa; MatematikThis 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.Article Citation - WoS: 11Citation - Scopus: 14Numerical and Bifurcations Analysis for Multi Order Fractional Model of Hiv Infection of Cd4<sup>+</Sup>t-cells(Univ Politehnica Bucharest, Sci Bull, 2016) Alipour, Mohsen; Arshad, Sadia; Baleanu, DumitruIn this paper, we solve the dynamical system of HIV infection of CD4(+) T cells within the multi-order fractional derivatives. The Bernstein operational matrices in arbitrary interval [a,b] are applied to obtain the approximate analytical solution of the model. In this way, the fractional differential equations are reduced to an algebraic easily solvable system. The obtained solutions are accurate and the method is very efficient and simple in implementation. With the help of bifurcation analysis, we acquired the critical value of viral death rate, that is, if viral death rate is greater than the critical value then level of virus particles starts to decline and thus free virus will eventually eliminate and patient is cured. Further, we found the threshold for viral infection rate analytically, which assures the stability of uninfected equilibrium and virus will ultimately eradicate.