Financial market volatility is crucial for pricing volatility derivatives. Log-volatility acts like a fractional Brownian motion with a small Hurst exponent. A model combining log-normal SABR with fractional stochastic volatility accurately values variance and volatility swaps. The fair strike price of variance swaps is solved exactly using fractional Ito calculus, while an approximate solution is found for volatility swaps. The model outperforms Heston and traditional SABR models in calibrating to market variance swap rates.