Accurate solution of the Thomas-Fermi equation using the fractional order of rational Chebyshev functions

In this paper, the nonlinear singular Thomas-Fermi differential equation for neutral atoms is solved using the fractional order of rational Chebyshev orthogonal functions (FRCs) of the first kind, FTnα(t,L), on a semi-infinite domain, where L is an arbitrary numerical parameter. First, using the quasilinearization method, the equation be converted into a sequence of linear ordinary differential equations (LDEs), and then these LDEs are solved using the FRCs collocation method. Using 300 collocation points, we have obtained a very good approximation solution and the value of the initial slope y′(0)=−1.5880710226113753127186845094239501095, highly accurate to 37 decimal places.