This work aims to propose a new analyzing tool, called the fractional iteration algorithm I for finding numerical solutions of nonlinear time fractional-order Cauchy reaction-diffusion model equations. The key property of the suggested technique is its ability and flexibility to investigate linear and nonlinear models conveniently and accurately. The proposed approach can be utilized without the use of any transformation, Adomian polynomials, small perturbation, discretization or linearization. The main feature of the fractional iteration algorithm-I is the improvement of an auxiliary parameter that can ensure a rapid convergence. To check the stability, accuracy and speed of the method, obtained results are compared numerically and graphically with the exact solutions and results available in the latest literature. In addition, numerical results are displayed graphically for various cases of the fractional-order $\alpha$. These results demonstrate the viability of the proposed technique and show that this technique is exceptionally powerful and suitable for solving fractional PDEs.

这项工作旨在提出一种新的分析工具，称为分数迭代算法I，用于寻找非线性时间分数阶柯西反应扩散模型方程的数值解。所建议技术的关键特性是其方便，准确地研究线性和非线性模型的能力和灵活性。可以在不使用任何变换，Adomian多项式，小扰动，离散化或线性化的情况下使用所提出的方法。分数迭代算法-I的主要特征是可确保快速收敛的辅助参数的改进。为了检查方法的稳定性，准确性和速度，将获得的结果在数值和图形上与最新文献中提供的确切解决方案和结果进行比较。此外，$\alpha$。这些结果证明了所提出技术的可行性，并表明该技术异常强大并且适用于解决分数PDE。