[en] The present article highlights the inconsistency of static Woods–Saxon potential and the applicability of energy dependent Woods–Saxon potential to explore the fusion dynamics of ${}_{22}^{48}Ti{+}^{58,60,64}{}_{28}Ni,{}_{22}^{46}Ti+{}_{28}^{64}Ni,{}_{22}^{50}Ti+{}_{28}^{60}Ni$, and ${}_9^{19}F{+}_{41}^{93}Nb$ reactions leading to formation of different Sn-isotopes via different entrance channels. Theoretical calculations based upon one-dimensional Wong formula obtained by using static Woods–Saxon potential unable to provide proper explanation for sub-barrier fusion enhancement of these projectile-target combinations. However, the predictions of one-dimensional Wong formula based upon energy dependent Woods–Saxon potential model (EDWSP model) accurately describe the observed fusion dynamics of these systems wherein the significantly larger value of diffuseness parameter ranging from a = 0.85 fm to a = 0.97 fm is required to address the experimental data in whole range of energy. Therefore, the energy dependence in nucleus-nucleus potential simulates the influence of the nuclear structure degrees of freedom of the colliding pairs. (paper)