A STUDY ON THE k-GENERALIZATIONS OF SOME KNOWN FUNCTIONS AND FRACTIONAL OPERATORS

Abstract

In this paper, we first draw attention to the relationships between the original definitions and their k-generalizations of some known functions and fractional operators. Using these relationships, we not only easily reacquired the results which can be found in the existing literature for the k generalizations, but also show how to achieve new results with the help of known properties of the original functions and operators. We conclude our paper by observing that, since the definitions of k-generalizations are closely related to the original definitions (that is, the k = 1 case), most of the formulas and results for the k = 1 case can be translated rather trivially and simply by appropriate parameter and notational changes to hold true for the corresponding k-case.