In this article, we explore the effectiveness of two polynomial methods in solving non-linear time and space fractional partial differential equations. We first outline the general methodology and then apply it to five distinct experiments. The proposed method, noted for its simplicity, demonstrates a high degree of accuracy. Comparative analysis with existing techniques reveals that our approach yields more precise solutions. The results, presented through graphs and tables, indicate that He's and Daftardar-Jafari polynomials significantly enhance accuracy. Additionally, we provide an in-depth discussion on the computational costs associated with these polynomials. Due to its straightforward implementation, the proposed method can be extended for application to a broader range of problems.

翻译：本文探讨了两种多项式方法在求解非线性时空分数阶偏微分方程中的有效性。我们首先概述了一般方法论，随后将其应用于五个不同的实验。所提出的方法以其简洁性著称，展现出高度的精确性。与现有技术的比较分析表明，我们的方法能产生更精确的解。通过图表呈现的结果表明，He's 和 Daftardar-Jafari 多项式显著提高了精度。此外，我们对这些多项式相关的计算成本进行了深入讨论。由于其实现简单，所提出的方法可以扩展应用于更广泛的问题领域。