In this paper, we propose an adaptive framework for the variable power of the fractional least mean square (FLMS) algorithm using the concept of instantaneous error energy. The proposed algorithm named variable power-FLMS (VP-FLMS) is computationally less expensive and dynamically adapts the fractional power of the FLMS to achieve a high convergence rate with a low steady state error. For the evaluation purpose, the problems of channel estimation and channel equalization are considered. The experiments clearly show that the proposed approach achieves better convergence rate and lower steady-state error compared to the FLMS.