Conventional adaptive filters, which assume Gaussian distribution for signal and noise, exhibit significant performance degradation when operating in non-Gaussian environments. Recently proposed fractional-order adaptive filters (FoAFs) address this concern by assuming that the signal and noise are symmetric α-stable random processes. However, the literature does not include any VLSI architectures for these algorithms. Toward that end, this article develops hardware-efficient architecture for fractional-order correntropy adaptive filter (FoCAF). We first reformulate the FoCAF for its efficient real-time VLSI implementation and then demonstrate that these reformulations cause negligible performance degradation under the 16-bit fixed-point implementation.