  This article is devoted to the study of high dense charged anisotropic
compact structures in the framework of $f(R,\mathcal{T})$ gravity theory. The
principal aims of this investigation, regard the extension of the isotropic
Durgapal-Fuloria model within the context of charged isotropic
$f(R,\mathcal{T})$ solutions. The second main goal of this work is to apply the
gravitational decoupling via a minimal geometric deformation (MGD) scheme in
$f(R,\mathcal{T})$ gravity. Finally, the third one is to derive an anisotropic
version of the charged isotropic model previously obtained by applying
gravitational decoupling technology. This MGD approach splits the system of
equations into two separate sets, one corresponding with the f(R,$\mathcal{T}$)
gravity system and another corresponding to the anisotropic sector governed by
the extra source $\theta_{\mu\nu}$.To address this task we have considered some
ingredients: I) the f(R,$\mathcal{T}$) model corresponds to a linear functional
of the Ricci's scalar and the trace of the energy-momentum tensor
$\mathcal{T}$, specifically $ f(R,\mathcal{T}) =R+2\chi\mathcal{T}$, being
$\chi$ a running coupling constant. II) The matter distribution is taken to be
an isotropic fluid one, III) the Lagrangian matter $\mathcal{L}_{m}$
corresponds to the negative isotropic pressure \i.e, $-p$ and IV) in order to
solve the $\theta$-sector, a suitable form for the decoupler function $f(r)$
has been imposed, respecting all the physical and mathematical requirements.
  Finally, to check and contrast our model an exhaustive mathematical, physical
and graphical analysis is performed in order to show all the properties that
characterize the compact structure. It is worth mentioning that when $\chi=0$
Einstein's gravity theory results are recovered.

General Relativity and Quantum Cosmology