Hacettepe Journal of Mathematics and Statistics 2651-477X 2651-477X Hacettepe University Mathematical Sciences Matematik An efficient numerical method for solving nonlinear astrophysics equations of arbitrary order https://orcid.org/0000-0001-6632-4743 Delkhosh Mehdi Shahid Beheshti University https://orcid.org/0000-0001-5946-0771 Parand Kourosh Shahid Beheshti University 12 08 2019 48 6 1601 1619 11 02 2017 05 16 2018 Copyright © 2002, Hacettepe Journal of Mathematics and Statistics 2002 Hacettepe Journal of Mathematics and Statistics

The Lane-Emden type equations of arbitrary (fractional and integer) order and the white dwarf equation are employed in the modeling of several phenomena in the areas of mathematical physics and astrophysics. In this paper, an efficient numerical algorithm based on the generalized fractional order of the Chebyshev orthogonal functions (GFCFs) and the collocation method to solve these well-known differential equations is presented. The operational matrices of the fractional derivative and the product of order $\alpha$ in the Caputo's definition for the GFCFs are used. The obtained results are compared with other results to verify the accuracy and efficiency of the presented method. The obtained numerical results are better than other proposed methods.

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