The main aim of this paper is to analyze the behavior of time-fractional Emden–Fowler (EF) equation associated with Caputo–Katugampola fractional derivative occurring in mathematical physics and astrophysics. A powerful analytical approach, which is an amalgamation of q-homotopy analysis approach and generalized Laplace transform with homotopy polynomials, is implemented to obtain approximate analytical solution of the time-fractional EF equation. Main advantage of this research work is that the implemented technique contains an auxiliary parameter to control the convergence region of obtained series solution. Some examples are considered to illustrate the accuracy and efficiency of the applied technique. Numerical results are demonstrated in the form of tabular and graphical representations.

本文的主要目的是分析数学物理和天体物理学中与 Caputo-Katugampola 分数阶导数相关的时间分数 Emden-Fowler (EF) 方程的行为。采用一种强大的分析方法，该方法结合了 q 同伦分析方法和具有同伦多项式的广义拉普拉斯变换，以获得时间分数 EF 方程的近似解析解。这项研究工作的主要优点是所实现的技术包含一个辅助参数来控制所获得的级数解的收敛区域。考虑一些例子来说明所应用技术的准确性和效率。数值结果以表格和图形表示的形式展示。