共形分数等温气体球
Conformable Fractional Isothermal Gas Spheres
摘要：
等温气体球是天体物理学、物理学、化学和工程学中模拟许多问题的有力工具。该奇异微分方程没有精确解，只能用数值方法和近似方法求解。在本文中，在牛顿流体静力平衡的框架内，我们发展了分数等温气体球的一般解析公式。为了获得质量、半径和密度的解析表达式，除了分数等温气体球，我们还使用了一致分数微积分。利用级数展开法，我们得到了一个一般的递推关系，它使我们能够确定级数系数。对于分数参数α=1，级数解与数值解的比较对于维数参数x=3.2是好的，超过这个值，级数发散。我们应用Euler-Abel和Pade技术的组合来加速级数，因此加速级数收敛到数值期望值。分析了一个典型中子星模型的质量半径关系、密度、压比等物理参数。我们发现，目前的模型符合中子星有较小的体积和质量比这两个恒星的修改的黎曼-刘维导数的上下文中，以及整数。
英文摘要：
The isothermal gas sphere is well known as a powerful tool to model many problems in astrophysics, physics, chemistry, and engineering. This singular differential equation has not an exact solution and solved only by numerical and approximate methods. In the present paper and within the framework of the Newtonian hydrostatic equilibrium, we have developed general analytical formulations for the fractional isothermal gas sphere. To obtain analytical expressions for mass, radius, and density, besides the fractional isothermal gas sphere, we used the conformable fractional calculus. Using the series expansion method, we obtained a general recurrences relation, which allows us to determine the series coefficients. The comparison of the series solution with the numerical ones for the fractional parameter α=1 is good for dimensional parameters up to x=3.2, beyond this value, the series diverges. We applied a combination of Euler-Abel and Pade techniques to accelerate the series, therefore accelerated series converge to the numerical desired value. We analyzed some physical parameters of a typical model of the neutron stars such as the mass-radius relation, density, and pressure ratio for different models. We found that the current models of the conformable neutron stars had smaller volumes and masses than both stars in the context of modified Rienmann-Liouville derivatives as well as the integer one.
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。
