  In this paper, we consider a non-static spherical geometry and formulate its
extension for the case of anisotropic matter configuration through minimal
gravitational decoupling in $f(\mathbb{R},\mathbb{T})$ theory. We apply a
particular transformation only on the radial metric function that divides the
modified field equations into two distinct sectors corresponding to their
parent (original and additional) sources. The unknowns in the first (isotropic)
set are reduced by taking the Friedmann-Lemaitre-Robertson-Walker cosmic model.
We then obtain the isotropic solution by employing a linear equation of state
and power-law form of the scale factor. The other set involves the decoupling
function and components of an extra source, therefore we adopt a density-like
constraint to close it. Finally, we analyze the role of this modified gravity
and the decoupling parameter on three different eras of the cosmos by
graphically observing the developed extended solution. It is concluded that the
resulting solutions fulfill all the physical requirements only for the matter
and radiation-dominated eras.
