We study a fractional-order model for the anthrax disease between animals based on the Caputo–Fabrizio derivative. First, we derive an existence criterion of solutions for the proposed fractional \(\mathcal {CF}\)-system of the anthrax disease model by utilizing the Picard–Lindelof technique. By obtaining the basic reproduction number \(\mathcal{R}_{0}\) of the fractional \(\mathcal{CF}\)-system we compute two disease-free and endemic equilibrium points and check the asymptotic stability property. Moreover, by applying an iterative approach based on the Sumudu transform we investigate the stability of the fractional \(\mathcal{CF}\)-system. We obtain approximate series solutions of this system by means of the homotopy analysis transform method, in which we invoke the linear Laplace transform. Finally, after the convergence analysis of the numerical method HATM, we present a numerical simulation of the \(\mathcal{CF}\)-fractional anthrax disease model and review the dynamical behavior of the solutions of this \(\mathcal {CF}\)-system during a time interval.

我们基于Caputo–Fabrizio衍生物研究了动物之间炭疽病的分数阶模型。首先，我们利用Picard-Lindelof技术推导了所提出的炭疽病模型分数\（\ mathcal {CF} \）-系统的解的存在性准则。通过获得分数\（\ mathcal {CF} \）-系统的基本繁殖数\（\ mathcal {R} _ {0} \），我们计算出两个无病的地方病平衡点，并检查了渐近稳定性。此外，通过应用基于Sumudu变换的迭代方法，我们研究了分数\（\ mathcal {CF} \）的稳定性-系统。通过同伦分析变换方法，我们获得了该系统的近似级数解，其中我们调用了线性拉普拉斯变换。最后，在对数值方法HATM进行收敛性分析之后，我们对\（\ mathcal {CF} \）-分数炭疽病模型进行了数值模拟，并回顾了该\（\ mathcal {CF}的解的动力学行为。\）-在一定时间间隔内的系统。