The conditional expectation E(Y vertical bar X) of a generalized functional linear model with scalar response Y is given by g{(X, phi)(L2)} where X and phi are functions defined in L-2 := L-2[0, 1]. Let us consider that X belongs to the Sobolev space W := W-2,W-1 [0, 1] and denote X' its derivative. In this paper we focus on an extension of the previous model where E(Y vertical bar X) is given by g{< X, beta >(W) + < X', gamma >(L2)). With a similar approach to Cardot and Sarda (2005) or Stone (1986) for generalized additive models, we propose estimators for the unknown parameters beta, gamma and obtain their rate of convergence. We compare numerically the prediction performance of this new model with alternative models proposed in the literature.