In this paper vibration damping capacity of shape memory alloys (SMA) is studied, whose constitutive behavior is based on two dimensional Oberaigner, Fischer and Tanaka model (Oberaigner et al., 2002). The active and passive vibration damping paradigms of SMA with respect to thermal changes are touched here. In this worktime-fractional order is given here. The above model solution is presented here for the most general case of a set of initial and boundary conditions which deal with generalized mechanical loadings and thermal regimes. For the particular cases, four examples for different thermal and mechanical loading-stresses, endorsed on the basis of fractional order with Homotopy Perturbation Method (HPM), are given. The solution given in this paper tells us how vibration response is studied with different thermal and different types of static and dynamic mechanical loading scenarios. (C) 2017 Elsevier Ltd. All rights reserved.