As the communication systems have been increasingly complex, the problem of channel estimation for such complex communication systems has also emerged as an equally challenging task. To solve this problem, various schemes based on Least Mean Square (LMS) and its improved variants have been proposed. This paper presents an adaptive algorithm for channel estimation in non-Gaussian environment. The proposed algorithm named as fractional least mean fourth (FLMF) is derived using the concept of fractional order calculus (FOC) and least mean fourth (LMF). The proposed algorithm is a convex combination of conventional and fractional order gradient descent method and by removing the computationally expensive Gamma function from fractional gradient it become not only computationally inexpensive but also achieves the high convergence rate with low steady state error. The proposed algorithm is evaluated for the channel estimation problem in multiple configurations and it achieves better results compared to both the fractional least mean square (FLMS) and the least mean fourth (LMF) algorithms.