Five-Parameter Discrete ML Function and Corresponding Discrete Double Fractional Operator

In recent years, discrete Mittag-Leffler (ML) functions have been investigated intensively since they are connected with the discrete fractional calculus and have interesting application in applied sciences. In this study, inspired by the five-parameter ML function by {"O}zarslan et. al.\cite{OzarslanArran}, we define its discrete version, namely five-parameter discrete ML function. We explore various characteristics, such as the double fractional sum and difference, of the discrete ML function with five parameters. Then, using the mentioned discrete function, we introduce the discrete double fractional operator having this function through the semigroup property. We also obtain the left inverse operator which is the corresponding discrete difference operator for the discrete double fractional operator.