  The current cosmic time evolution of the Universe is described by the General
Relativity theory when a cosmological principle is considered under a flat
space time landscape. The set of known as Friedmann equations, contain the
principles that lead to the construction of the standard $\Lambda$CDM model.
However, the current state-of-art regarding these equations, even if it is a
fundamental method, is based in solving analytically the differential equations
by considering several forms of matter/energy components or evaluating them in
specific cosmic times where two or more components contribute at the same rate.
This latter can be carry out through the approach of piecewice solutions, whose
reduce the numerical integrals. In this paper we discuss new solutions through
special analytical functions and constraint them with an updated compilation of
observational Hubble observations in order to deal with the local $H_0$ tension
reported.
