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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| Vydáno v: | Fractal and fractional Ročník 6; číslo 6; s. 297 |
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01.06.2022
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| Abstract | 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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| AbstractList | 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. |
| Author | Kumar, Dinesh Choi, Junesang Ram, Jeta |
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| Cites_doi | 10.1016/j.jmaa.2007.03.018 10.4236/am.2016.714129 10.1080/00029890.1975.11993837 10.1016/B978-0-12-385218-2.00002-5 10.1016/0377-0427(94)90047-7 10.1080/01621459.1983.10478022 10.1137/0518043 10.1007/BF02403202 10.26637/mjm204/008 10.3390/math8081320 10.1002/mana.19720530114 10.1137/0117013 10.1016/j.jat.2009.05.002 10.3934/math.2020094 10.1080/10652460310001600717 10.1007/978-1-4419-0916-9 10.1007/978-3-662-61550-8 10.1016/0022-247X(63)90067-2 10.1016/0021-9045(91)90006-V |
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| Snippet | 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... |
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| SubjectTerms | 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 |
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| Title | Dirichlet Averages of Generalized Mittag-Leffler Type Function |
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