This paper deals with the numerical solutions and convergence analysis for general
singular Lane–Emden type models of fractional order, with appropriate constraint initial conditions.
A modified reproducing kernel discretization technique is used for dealing with the fractional
Atangana–Baleanu–Caputo operator. In this tendency, novel operational algorithms are built and
discussed for covering such singular models in spite of the operator optimality used. Several numerical
applications using the well-known fractional Lane–Emden type models are examined, to expound the
feasibility and suitability of the approach. From a numerical viewpoint, the obtained results indicate
that the method is intelligent and has several features stability for dealing with many fractional
models emerging in physics and mathematics, using the new presented derivative.