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

被引：14

作者：

Ozarslan, Mehmet Ali ^{[1
]}

Fernandez, Arran ^{[1
]}

机构：

[1] Eastern Mediterranean Univ, Fac Arts & Sci, Dept Math, Via Mersin 10, TR-99628 Famagusta, Northern Cyprus, Turkey

来源：

FRACTAL AND FRACTIONAL | 2021年 / 5卷 / 02期

关键词：

Mittag-Leffler functions; fractional integrals; fractional derivatives; Abel equations; Laplace transforms; mixed partial derivatives; DIFFERENTIAL-EQUATIONS; INTEGRAL-EQUATION; POLYNOMIALS;

D O I：

10.3390/fractalfract5020045

中图分类号：

O1 [数学];

学科分类号：

0701 ; 070101 ;

摘要：

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

引用

页数：22

共 52 条

[1] Trivariate Mittag-Leffler functions used to solve multi-order systems of fractional differential equations [J].