Generalized shift operators and pseudo-polynomials of fractional order

We introduce families of pseudo-Kampe de Feriet polynomials, which can be viewed as the natural complement for the theory of fractional derivatives and partial fractional differential equations of evolutive type. We show that they allow the possibility of treating a large variety of exponential operators, providing generalized fractional forms of shift operators. The link of these pseudo-polynomials with Wright-type functions is also discussed. (C) 2002 Elsevier Science Inc. All rights reserved.