分数多变气体球的解析解
Analytical Solution to the Fractional Polytropic Gas Spheres
摘要：
Lane-Emden方程可以用来模拟恒星内部、星团以及天体物理中的许多构型。不幸的是，只有多方指数和的精确解。本文给出分数阶Lane-Emden方程的级数解。在修正的Rienmann-Liouville导数框架下求解。所得结果恢复了著名的级数解。对n=3的分数阶模型进行了计算，研究了质量半径关系、密度比、压力比和温度比。我们发现分数星比整数星有更小的体积和质量。
英文摘要：
Lane-Emden equation could be used to model stellar interiors, star clusters and many configurations in astrophysics. Unfortunately, there is an exact solution only for the polytropic index and . In the present paper, a series solution for the fractional Lane-Emden equation is presented. The solution is performed in the frame of modified Rienmann Liouville derivatives. The obtained results recover the well-known series solutions when . Fractional model of n=3 has been calculated and mass-radius relation, density ratio, pressure ratio and temperature ratio have been investigated. We found that the fractional star has a smaller volume and mass than that of the integer star.
机构、总结、中文摘要均由AI分析而来，可能存在错误，请以论文正文为准。
