Scopus İndeksli Yayınlar Koleksiyonu
Permanent URI for this collectionhttps://hdl.handle.net/20.500.12416/8651
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Article Citation - WoS: 3Citation - Scopus: 5Simpson's Method for Fractional Differential Equations With a Non-Singular Kernel Applied To a Chaotic Tumor Model(Iop Publishing Ltd, 2021) Defterli, Ozlem; Tang, Yifa; Baleanu, Dumitru; Arshad, Sadia; Saleem, IramThis 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.Article Citation - WoS: 174Citation - Scopus: 199A New Fractional Modelling and Control Strategy for the Outbreak of Dengue Fever(Elsevier, 2019) Arshad, Sadia; Baleanu, Dumitru; Jajarmi, AminThis paper deals with a new mathematical model for a dengue fever outbreak based on a system of fractional differential equations. The equilibrium points and stability of the new system are studied. To simulate this model, a new and efficient numerical method is provided and its stability and convergence are proved. According to a real outbreak on the Cape Verde Islands occurred in year 2009, the new model is examined for a period of three months by using singular or nonsingular kernels in the definition of derivative operator. Simulation results show that the proposed formalism with exponential kernel agrees well with the real data in the early stage of the epidemic while the Mittag-Leffler kernel fits the reality for the later part of the time interval. Hence, the new framework in a hybrid manner can properly simulate the dynamics of the disease in the whole of the time interval. In order to stabilize the disease-free equilibrium point of the system under investigation, two control strategies are suggested. Numerical simulations verify that the proposed stabilizing controllers are efficient and provide significantly remarkable results. (C) 2019 Elsevier B.V. All rights reserved.Article Citation - WoS: 4Citation - Scopus: 4A Fourth Order Finite Difference Method for Time-Space Fractional Diffusion Equations(Global Science Press, 2018) Baleanu, Dumitru; Huang, Jianfei; Tang, Yifa; Zhao, Yue; Arshad, SadiaA 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.Article Citation - WoS: 27Citation - Scopus: 32Finite Difference Method for Time-Space Fractional Advection-Diffusion Equations With Riesz Derivative(Mdpi, 2018) Baleanu, Dumitru; Huang, Jianfei; Al Qurashi, Maysaa Mohamed; Tang, Yifa; Zhao, Yue; Arshad, SadiaIn 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.