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In this paper, we generalize the analysis of the $f(R,T)-$brane via theinclusion of a term proportional to the Gauss-Bonnet invariant. We consider anaction of the form $F(R,G,T)=f(R,T)+\alpha G$, where $T$ is the trace of thestress-energy tensor, $R$ is the Ricci scalar, and $\alpha$ is a real parameterthat controls the contribution of the Gauss-Bonnet invariant $G$. We introducethe first-order formalism to obtain solutions for the source field of the branein the special case where $f(R,T)=R+\beta T$ and illustrate its procedure withan application to the sine-Gordon model. We also investigate the general caseof the $f(R,T)-$brane via the use of the scalar-tensor formalism, where we alsouse the first-order formalism to obtain solutions. Finally, we investigate thelinear stability of the brane under tensor perturbations of the the modifiedEinstein's field equations. Our results indicate that the Gauss-Bonnet term mayinduce qualitatively different behaviors of the quantities on the brane,provided that its contribution is large enough.

Scalar-tensor representation to $f(R,T)-$brane with Gauss-Bonnet gravity