ANALOGUE OF THE SHIFT OPERATORS AND PSEUDO - POLYNOMIALS OF FRACTIONAL ORDER

he present paper envisages the q - analogues of the  operators, results determined by Dattoli et al, to deal with the families of pseudo-Kampé de Fériet polynomials, which can be viewed as the complement for the theory of q-fractional derivatives and q-partial fractional differential equations of evolutionary type.  We show that these families allow the possibility of treating a large variety of q-exponential operators providing generalized fractional forms of q-shift operators.