This paper extends the kernel affine projection algorithm to a rich, flexible and cohesive taxonomy of fractional signal processing approach. The formulation of the algorithm is established on the inclusion of Riemann–Liouville fractional derivative to gradient-based stochastic Newton recursive method to minimize the cost function of the kernel affine projection algorithm. This approach extends the idea of fractional signal processing in reproducing kernel Hilbert space. The proposed algorithm is applied to the prediction of chaotic Lorenz time series and nonlinear channel equalization. Also the performance is validated in comparison with the least mean square algorithm, kernel least mean square algorithm, affine projection algorithm and kernel affine projection algorithm.