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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| Format: | Article |
| Language: | English |
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MDPI AG
2022-05-01
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| Series: | Fractal and Fractional |
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| Online Access: | https://www.mdpi.com/2504-3110/6/6/297 |
| _version_ | 1797487293914677248 |
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| author | Dinesh Kumar Jeta Ram Junesang Choi |
| author_facet | Dinesh Kumar Jeta Ram Junesang Choi |
| author_sort | Dinesh Kumar |
| collection | DOAJ |
| description | 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 <i>R</i>-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. |
| first_indexed | 2024-03-09T23:46:32Z |
| format | Article |
| id | doaj.art-313d41481495491bbdbb66174fe65111 |
| institution | Directory Open Access Journal |
| issn | 2504-3110 |
| language | English |
| last_indexed | 2024-03-09T23:46:32Z |
| publishDate | 2022-05-01 |
| publisher | MDPI AG |
| record_format | Article |
| series | Fractal and Fractional |
| spelling | doaj.art-313d41481495491bbdbb66174fe651112023-11-23T16:42:21ZengMDPI AGFractal and Fractional2504-31102022-05-016629710.3390/fractalfract6060297Dirichlet Averages of Generalized Mittag-Leffler Type FunctionDinesh Kumar0Jeta Ram1Junesang Choi2Department of Applied Sciences, College of Agriculture-Jodhpur, Agriculture University Jodhpur, Jodhpur 342304, IndiaDepartment of Mathematics and Statistics, Jai Narain Vyas University, Jodhpur 342005, IndiaDepartment of Mathematics, Dongguk University, Gyeongju 38066, KoreaSince 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 <i>R</i>-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.https://www.mdpi.com/2504-3110/6/6/297Dirichlet averages<i>B</i>-splinesdirichlet splinesRiemann–Liouville fractional integralshypergeometric functions of one and several variablesgeneralized Mittag-Leffler type function |
| spellingShingle | Dinesh Kumar Jeta Ram Junesang Choi Dirichlet Averages of Generalized Mittag-Leffler Type Function Fractal and Fractional Dirichlet averages <i>B</i>-splines dirichlet splines Riemann–Liouville fractional integrals hypergeometric functions of one and several variables generalized Mittag-Leffler type function |
| title | Dirichlet Averages of Generalized Mittag-Leffler Type Function |
| title_full | Dirichlet Averages of Generalized Mittag-Leffler Type Function |
| title_fullStr | Dirichlet Averages of Generalized Mittag-Leffler Type Function |
| title_full_unstemmed | Dirichlet Averages of Generalized Mittag-Leffler Type Function |
| title_short | Dirichlet Averages of Generalized Mittag-Leffler Type Function |
| title_sort | dirichlet averages of generalized mittag leffler type function |
| topic | Dirichlet averages <i>B</i>-splines dirichlet splines Riemann–Liouville fractional integrals hypergeometric functions of one and several variables generalized Mittag-Leffler type function |
| url | https://www.mdpi.com/2504-3110/6/6/297 |
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