• Kourosh Parand Department of Cognitive Modelling, Institute for Cognitive and Brain Sciences, Shahid Beheshti University, G.C, Tehran, Iran
  • Mehdi Delkhosh Department of Computer Sciences, Shahid Beheshti University, G.C., Tehran, Iran



Fractional order of the Chebyshev functions, Lane-Emden type equations, Isothermal gas sphere equation, Collocation method, Nonlinear ODE


The Lane-Emden type equations are employed in the modeling of several phenomena in the areas of mathematical physics and astrophysics. These equations are categorized as non-linear singular ordinary differential equations on the semi-infinite domain. In this paper, the generalized fractional order of the Chebyshev orthogonal functions (GFCFs) of the first kind have been introduced as a new basis for Spectral methods, and also presented an effective numerical method based on the GFCFs and the collocation method for solving the nonlinear singular Lane-Emden type equations of various orders. Obtained results have compared with other results to verify the accuracy and efficiency of the presented method.


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: Article ID 534754, 10 pages.

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