A naturally emerging bivariate Mittag-Leffler function and associated fractional-calculus operators

Abstract

We define an analogue of the classical Mittag-Leffler function which is applied to two variables, and establish its basic properties. Using a corresponding single-variable function with fractional powers, we define an associated fractional integral operator which has many interesting properties. The motivation for these definitions is twofold: firstly their link with some fundamental fractional differential equations involving two independent fractional orders, and secondly the fact that they emerge naturally from certain applications in bioengineering.

References in corpus (4)

• On some new properties of fractional derivatives with Mittag-Leffler kernel
• The Prabhakar or three parameter Mittag--Leffler function: theory and application
• A practical guide to Prabhakar fractional calculus
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Cited by in corpus (5)

• Modeling Blood Alcohol Concentration Using Fractional Differential Equations Based on the $\psi$-Caputo Derivative
• Analyses of the contour integral method for time fractional subdiffusion-normal transport equation
• An initial-boundary problem for a mixed fractional wave equation
• On generalized Mittag-Leffler-type functions of two variables
• Finite bivariate biorthogonal I -- Konhauser polynomials