Abstract
A wide family of position‐dependent mass damped oscillators affected by an external potential is investigated. First, a Lagrangian formulation is introduced for the corresponding problem. The Lagrangian function is time‐dependent, and the problem cannot be approached with classical procedures because it lacks variational symmetries. Therefore, the variational ‐symmetry method is applied to find exact solutions. Variational ‐symmetries are determined for a family of potential functions, which lead to a one‐parameter family of exact solutions. The results are applied to particular examples corresponding to some interesting mass functions reported in the previous literature.
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