In this paper, we introduce two reliable efficient approximate methods for solving a class of fractional Lane–Emden equations with conformable fractional derivative (CL-M) which are the so-called conformable Homotopy–Adomian decomposition method (CH-A) and conformable residual power series method (CRP). Furthermore, the proposed methods express the solutions of the non-linear cases of the CL-M in terms of fractional convergent series in which its components can be computed in an easy manner. Finally, the results are given by graphs for each case of the CL-M at different values of α in order to demonstrate its accuracy, applicability, and efficiency.

中文翻译：

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求解分数阶导数一致的分数Lane-Emden方程的两种有效方法

在本文中，我们引入了两种可靠有效的近似方法来求解一类具有一致分数阶导数 (CL-M) 的分数式 Lane-Emden 方程，即所谓的一致同伦-Adomian 分解方法 (CH-A) 和一致残差幂级数法 (CRP)。此外，所提出的方法根据分数收敛级数来表达 CL-M 非线性情况的解，其中可以以简单的方式计算其分量。最后，结果由不同 α 值的 CL-M 每种情况的图表给出，以证明其准确性、适用性和效率。