Dirichlet Averages of Generalized Mittag-Leffler Type Function

Since Gösta Magus Mittag-Leffler introduced the so-called Mittag-Leffler function in 1903 and studied its features in five subsequent notes, passing the first half of the 20th century during which the majority of scientists remained almost unaware of the function, the Mittag-Leffler function and its...

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Veröffentlicht in:Fractal and fractional Jg. 6; H. 6; S. 297
Hauptverfasser: Kumar, Dinesh, Ram, Jeta, Choi, Junesang
Format: Journal Article
Sprache:Englisch
Veröffentlicht: Basel MDPI AG 01.06.2022
Schlagworte:
B-splines
Dirichlet averages
Dirichlet problem
dirichlet splines
Fractional calculus
generalized Mittag-Leffler type function
Hypergeometric functions
hypergeometric functions of one and several variables
Integrals
Mathematical analysis
Riemann–Liouville fractional integrals
ISSN:2504-3110, 2504-3110
Online-Zugang:Volltext
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Zusammenfassung:Since Gösta Magus Mittag-Leffler introduced the so-called Mittag-Leffler function in 1903 and studied its features in five subsequent notes, passing the first half of the 20th century during which the majority of scientists remained almost unaware of the function, the Mittag-Leffler function and its various extensions (referred to as Mittag-Leffler type functions) have been researched and applied to a wide range of problems in physics, biology, chemistry, and engineering. In the context of fractional calculus, Mittag-Leffler type functions have been widely studied. Since Carlson established the notion of Dirichlet average and its different variations, these averages have been explored and used in a variety of fields. This paper aims to investigate the Dirichlet and modified Dirichlet averages of the R-function (an extended Mittag-Leffler type function), which are provided in terms of Riemann-Liouville integrals and hypergeometric functions of several variables. Principal findings in this article are (possibly) applicable. This article concludes by addressing an open problem.
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ISSN:2504-3110
2504-3110
DOI:10.3390/fractalfract6060297