On the Duffin–Kemmer–Petiau equation with linear potential in the presence of a minimal length

Highlights: • We point out an erroneous treatment concerning the DKP equation in the presence of a minimal length. • A deformed version of the DKP equation, including the first-order effect of the minimal length, is constructed. • First-order effects of the minimal length are calculated when a Lorentz-scalar linear potential is applied. - Abstract: We point out an erroneous handling in the literature regarding solutions of the $(1+1)$-dimensional Duffin–Kemmer–Petiau equation with linear potentials in the context of quantum mechanics with minimal length. Furthermore, using Brau's approach, we present a perturbative treatment of the effect of the minimal length on bound-state solutions when a Lorentz-scalar linear potential is applied.