Scopus İndeksli Yayınlar Koleksiyonu
Permanent URI for this collectionhttps://hdl.handle.net/20.500.12416/8651
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Article Analysis of the model of HIV-1 infection of CD4(+) T-cell with a new approach of fractional derivative(Springer, 2020) Baleanu, Dumitru; Mohammadi, Hakimeh; Rezapour, ShahramBy using the fractional Caputo-Fabrizio derivative, we investigate a new version for the mathematical model of HIV. In this way, we review the existence and uniqueness of the solution for the model by using fixed point theory. We solve the equation by a combination of the Laplace transform and homotopy analysis method. Finally, we provide some numerical analytics and comparisons of the results.Article Comparative Study for Optimal Control Nonlinear Variable-Order Fractional Tumor Model(Elsevier LTD., 2020) Sweilam, N. H.; Al-Mekhlafi, S. M.; Alshomrani, Ali Saleh; Baleanu, DumitruArticle Asymptotic Integration of (1 + Α) -Order Fractional Differential Equations(Pergamon-Elsevier Science Ltd, 2011) Baleanu, Dumitru; Mustafa, Octavian G.; Agarwal, Ravi P.; Bleanu, DumitruWe establish the long-time asymptotic formula of solutions to the (1+α)-order fractional differential equation 0iOt1+αx+a(t)x=0, t>0, under some simple restrictions on the functional coefficient a(t), where 0iOt1+α is one of the fractional differential operators 0Dtα(x′), (0Dtαx)′= 0Dt1+αx and 0Dtα(tx′-x). Here, 0Dtα designates the Riemann-Liouville derivative of order α∈(0,1). The asymptotic formula reads as [b+O(1)] ·xsmall+c·xlarge as t→+∞ for given b, c∈R, where xsmall and xlarge represent the eventually small and eventually large solutions that generate the solution space of the fractional differential equation 0iOt1+αx=0, t>0Article Research Article On Fractional SIRC Model with Salmonella Bacterial Infection(Hindawi LTD, 2014) Baleanu, Dumitru; Rihan, Fathalla A.; Lakshmanan, S.; Rakkiyappan, R.We propose a fractional order SIRC epidemic model to describe the dynamics of Salmonella bacterial infection in animal herds. The infection-free and endemic steady sates, of such model, are asymptotically stable under some conditions. The basic reproduction number R-0 is calculated, using next-generation matrix method, in terms of contact rate, recovery rate, and other parameters in the model. The numerical simulations of the fractional order SIRC model are performed by Caputo's derivative and using unconditionally stable implicit scheme. The obtained results give insight to the modelers and infectious disease specialists.Article A New Impulsive Multi-Orders Fractional Differential Equation Involving Multipoint Fractional Integral Boundary Conditions(Hindawi LTD, 2014) Wang, Guotao; Liu, Sanyang; Zhang, Lihong; Baleanu, DumitruA new impulsive multi-orders fractional differential equation is studied. The existence and uniqueness results are obtained for a nonlinear problem with fractional integral boundary conditions by applying standard fixed point theorems. An example for the illustration of the main result is presented.