  In the present work, we attempt to find a new class of solutions for the
spherically symmetric perfect fluid sphere by employing the Homotopy
Perturbation Method (HPM), a new tool via which the mass polynomial function
facilitates to tackle the Einstein field equations. A set of interior solutions
found on the basis of the simplest MIT bag model equation of state (EOS) in the
form $p=\frac{1}{3}(\rho-4B)$ where $B$ is the bag constant. The proposed
interior metric for the stellar system is consistent with the exterior
Schwarzschild spacetime on the boundary. In addition, we also conduct a
detailed study on different tests, viz. the energy conditions, TOV equation,
adiabatic index, Buchdahl limit, etc., to verify the physical validity of the
proposed model. The numerical value of the used parameters is predicted for
different strange star candidates, for different chosen values of the bag
constant. In a nutshell, by exploiting HPM technique first time ever in the
field of relativistic astrophysics, we have predicted in the present literature
a singularity-free and stable stellar model which is suitable to describe
ultra-dense objects, like strange (quark) stars.
