We study a specific model of anisotropic strange stars in the modified $fleft(R,mathcal{T}right)$-type gravity by deriving solutions to the modified Einstein field equations representing a spherically symmetric anisotropic stellar object. We take a standard assumption that $f(R,mathcal{T})=R+2chimathcal{T}$, where $R$ is Ricci scalar, $mathcal{T}$ is the trace of the energy-momentum tensor of matter, and $chi$ is a coupling constant. To obtain our solution to the modified Einstein equations, we successfully apply the `embedding class 1 techniques. We also consider the case when the strange quark matter (SQM) distribution is governed by the simplified MIT bag model equation of state given by $p_r=frac{1}{3}left(rho-4Bright)$, where $B$ is bag constant. We calculate the radius of the strange star candidates by directly solving the modified TOV equation with the observed values of the mass and some parametric values of $B$ and $chi$. The physical acceptability of our solutions is verified by performing several physical tests. Interestingly, besides the SQM, another type of matter distribution originates due to the effect of coupling between the matter and curvature terms in the $fleft(R,mathcal{T}right)$ gravity theory. Our study shows that with decreasing the value of $chi$, the stellar systems under investigations become gradually massive and larger in size, turning them into less dense compact objects. It also reveals that for $chi<0$ the $fleft(R,mathcal{T}right)$ gravity emerges as a suitable theory for explaining the observed massive stellar objects like massive pulsars, super-Chandrasekhar stars and magnetars, etc., which remain obscure in the standard framework of General Relativity (GR).
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