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Mittag-Leffler type functions of three variables
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In this article, we generalized Mittag-Leffler-type functions F ̵̄ A ( 3 )
, F ̵̄ B ( 3 ) , F ̵̄ C ( 3 ) and F ̵̄ D ( 3 ) , which correspond,
respectively, to the familiar Lauricella hypergeometric functions F A (
3 ) , F B ( 3 ) , F C ( 3 ) and F D ( 3 ) of three variables. Among the
various properties and characteristics of these three-variable
Mittag-Leffler-type function F ̵̄ D ( 3 ) , which we investigate in this
article, include their relationships with other extensions and
generalizations of the classical Mittag-Leffler functions, their
three-dimensional convergence regions, their Euler-type integral
representations, their Laplace transforms, their connections with the
Riemann-Liouville operators of fractional calculus, and the systems of
partial differential equations which are associated with them.
Title: Mittag-Leffler type functions of three variables
Description:
In this article, we generalized Mittag-Leffler-type functions F ̵̄ A ( 3 )
, F ̵̄ B ( 3 ) , F ̵̄ C ( 3 ) and F ̵̄ D ( 3 ) , which correspond,
respectively, to the familiar Lauricella hypergeometric functions F A (
3 ) , F B ( 3 ) , F C ( 3 ) and F D ( 3 ) of three variables.
Among the
various properties and characteristics of these three-variable
Mittag-Leffler-type function F ̵̄ D ( 3 ) , which we investigate in this
article, include their relationships with other extensions and
generalizations of the classical Mittag-Leffler functions, their
three-dimensional convergence regions, their Euler-type integral
representations, their Laplace transforms, their connections with the
Riemann-Liouville operators of fractional calculus, and the systems of
partial differential equations which are associated with them.
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