The objective of this paper is applying the well-known exact operational matrices (EOMs) idea for solving the Emden-Fowler equations, illustrating the superiority of EOMs over ordinary operational matrices (OOMs). Up to now, a few studies have been conducted on EOMs ; but the solved differential equations did not have high-degree nonlinearity and the reported results could not strongly show the...

Working within the deep-MOND limit (DML), I describe spherical, self-gravitating systems governed by a polytropic equation of state, $P=\mathcal{K}\rho^\gamma$. As self-consistent structures, such can serve as heuristic models for DML, astronomical systems, dwarf spheroidal galaxies, low-surface-density elliptical galaxies and star clusters, diffuse galaxy groups. They also testing ground vario...

In this paper, a new shifted ultraspherical wavelets operational matrix of derivatives is introduced. The two wavelets operational matrices, namely Legendre and first kind Chebyshev operational matrices can be deduced as two special cases. Two numerical algorithms based on employing the shifted ultraspherical wavelets operational matrix of derivatives for solving linear and nonlinear differenti...

A few questions related to white dwarfs' physics is posed. It seems that the modified gravity framework can be a good starting point provide alternative explanations cooling processes, their age determination, and Chandrasekhar mass limits. Moreover, we have also obtained limit coming from Palatini $f(\mathcal{R})$ provided by simple Lane-Emden model.

We give the description of nonlinear nonautonomous ordinary differential equations of order n with a so-called reducible linear part. The group classification of generalized Emden-Fowler equations of the mentioned class is done. We have found such laws of the variation of f(x) that the equation admits one, two, or tree one-parameter Lie groups.