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In this paper, the fractional order of rational Bessel functions collocationmethod (FRBC) to solve Thomas-Fermi equation which is defined in thesemi-infinite domain and has singularity at $x = 0$ and its boundary conditionoccurs at infinity, have been introduced. We solve the problem on semi-infinitedomain without any domain truncation or transformation of the domain of theproblem to a finite domain. This approach at first, obtains a sequence oflinear differential equations by using the quasilinearization method (QLM),then at each iteration solves it by FRBC method. To illustrate the reliabilityof this work, we compare the numerical results of the present method with somewell-known results in other to show that the new method is accurate, efficientand applicable.

A new approach for solving nonlinear Thomas-Fermi equation based on fractional order of rational Bessel functions