Existence theory and numerical simulation of HIV-I cure model with new fractional derivative possessing a non-singular kernel
Existence theory and numerical simulation of HIV-I cure model with new fractional derivative possessing a non-singular kernel
复制标题
非奇异核新分数阶导数HIV-I治愈模型的存在论与数值模拟
DOI：
10.1186/s13662-019-2336-5
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发表时间：
2019-09-23
影响因子：
4.1
通讯作者：
Baleanu, Dumitru
中科院分区：
文献类型：
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作者：
Aliyu, Aliyu Lsa;Alshomrani, Ali Saleh;Baleanu, Dumitru
本文从分数阶微积分的观点出发，研究了一个由三个种群组成的HIV-1感染治疗的数学模型。分数版本的模型正在考虑已被提出。所提出的模型进行了检查，使用Atangana-Baleanu分数算子的Caputo意义（ABC）。利用Picard-Lindelöf理论证明了分数阶模型的特解的存在唯一性。进一步证明了非负超平面是模型的正不变区域。最后，为了分析结果，通过最近设计的一种数值方法来寻找分数阶动力系统的近似解，进行了数值模拟。数值模拟结果表明，分数阶模型比经典模型具有更高的精度。所有必要的计算都是使用MATLAB R2018 a进行的，具有双精度运算。
In this research work, a mathematical model related to HIV-I cure infection therapy consisting of three populations is investigated from the fractional calculus viewpoint. Fractional version of the model under consideration has been proposed. The proposed model is examined by using the Atangana–Baleanu fractional operator in the Caputo sense (ABC). The theory of Picard–Lindelöf has been employed to prove existence and uniqueness of the special solutions of the proposed fractional-order model. Further, it is also shown that the non-negative hyper-planeis a positively invariant region for the underlying model. Finally, to analyze the results, some numerical simulations are carried out via a numerical technique recently devised for finding approximate solutions of fractional-order dynamical systems. Upon comparison of the numerical simulations, it has been demonstrated that the proposed fractional-order model is more accurate than its classical version. All the necessary computations have been performed using MATLAB R2018a with double precision arithmetic.