Laguerre functions extended to any real derivative orders

The differentiation orders of Laguerre polynomials and Laguerre functions are extended to permit non integer values. Using this new class of functions, a complete orthonormal basis is constructed. This basis is used to derive an identification method based on the generalised derivative Laguerre model. An academic example shows that the method can provide models with few parameters for systems with distributed time constants, and thus an improvement compared to integer order models.