On a Five-Parameter Mittag-Leffler Function and the Corresponding Bivariate Fractional Operators

Several extensions of the classical Mittag-Leffler function, including multi-parameter and multivariate versions, have been used to define fractional integral derivative operators. In this paper, we consider a function one variable with five parameters, special case Fox–Wright function. It turns out that most natural way based on requires considering it as two variables. This gives rise model bivariate calculus, which is useful in understanding differential equations involving mixed partial derivatives.