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Mittag-Leffler type functions of three variables
  • Hilola Yuldashova,
  • Anvar Hasanov
Hilola Yuldashova
Romanovsky Institute of Mathematics of the Academy of Sciences of the Republic of Uzbekistan

Corresponding Author:[email protected]

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Anvar Hasanov
Romanovsky Institute of Mathematics of the Academy of Sciences of the Republic of Uzbekistan
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Abstract

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.
Submitted to Mathematical Methods in the Applied Sciences
26 Jan 2024Review(s) Completed, Editorial Evaluation Pending
28 Jan 2024Reviewer(s) Assigned
03 Apr 2024Editorial Decision: Revise Major
29 Apr 20241st Revision Received
30 Apr 2024Review(s) Completed, Editorial Evaluation Pending
15 Jul 20242nd Revision Received
16 Jul 2024Submission Checks Completed
16 Jul 2024Assigned to Editor
16 Jul 2024Review(s) Completed, Editorial Evaluation Pending
24 Jul 2024Reviewer(s) Assigned
29 Jul 2024Editorial Decision: Accept