Certain New Chebyshev and Grüss-Type Inequalities for Unified Fractional Integral Operators via an Extended Generalized Mittag-Leffler Function
In this paper, by adopting the classical method of proofs, we establish certain new Chebyshev and Grüss-type inequalities for unified fractional integral operators via an extended generalized Mittag-Leffler function. The main results are more general and include a large number of available classical...
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| Format: | Article |
| Language: | English |
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MDPI AG
2022-03-01
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| Series: | Fractal and Fractional |
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| Online Access: | https://www.mdpi.com/2504-3110/6/4/182 |
| _version_ | 1797504805520801792 |
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| author | Wengui Yang |
| author_facet | Wengui Yang |
| author_sort | Wengui Yang |
| collection | DOAJ |
| description | In this paper, by adopting the classical method of proofs, we establish certain new Chebyshev and Grüss-type inequalities for unified fractional integral operators via an extended generalized Mittag-Leffler function. The main results are more general and include a large number of available classical fractional integral inequalities in the literature. Furthermore, some new fractional integral inequalities similar to the main results can be also obtained by employing the newly introduced generalized fractional integral operators involving the Mittag-Leffler-like function and weighted function. Consequently, their relevance with known inequalities for different kinds of fractional integral operators are pointed out. |
| first_indexed | 2024-03-10T04:09:35Z |
| format | Article |
| id | doaj.art-cdd2fda0c32e4abca228be4d2c10d2c8 |
| institution | Directory Open Access Journal |
| issn | 2504-3110 |
| language | English |
| last_indexed | 2024-03-10T04:09:35Z |
| publishDate | 2022-03-01 |
| publisher | MDPI AG |
| record_format | Article |
| series | Fractal and Fractional |
| spelling | doaj.art-cdd2fda0c32e4abca228be4d2c10d2c82023-11-23T08:15:13ZengMDPI AGFractal and Fractional2504-31102022-03-016418210.3390/fractalfract6040182Certain New Chebyshev and Grüss-Type Inequalities for Unified Fractional Integral Operators via an Extended Generalized Mittag-Leffler FunctionWengui Yang0Ministry of Public Education, Sanmenxia Polytechnic, Sanmenxia 472001, ChinaIn this paper, by adopting the classical method of proofs, we establish certain new Chebyshev and Grüss-type inequalities for unified fractional integral operators via an extended generalized Mittag-Leffler function. The main results are more general and include a large number of available classical fractional integral inequalities in the literature. Furthermore, some new fractional integral inequalities similar to the main results can be also obtained by employing the newly introduced generalized fractional integral operators involving the Mittag-Leffler-like function and weighted function. Consequently, their relevance with known inequalities for different kinds of fractional integral operators are pointed out.https://www.mdpi.com/2504-3110/6/4/182Chebyshev integral inequalityGrüss-type inequalitiessynchronous functionsMittag-Leffler functionunified fractional integral operators |
| spellingShingle | Wengui Yang Certain New Chebyshev and Grüss-Type Inequalities for Unified Fractional Integral Operators via an Extended Generalized Mittag-Leffler Function Fractal and Fractional Chebyshev integral inequality Grüss-type inequalities synchronous functions Mittag-Leffler function unified fractional integral operators |
| title | Certain New Chebyshev and Grüss-Type Inequalities for Unified Fractional Integral Operators via an Extended Generalized Mittag-Leffler Function |
| title_full | Certain New Chebyshev and Grüss-Type Inequalities for Unified Fractional Integral Operators via an Extended Generalized Mittag-Leffler Function |
| title_fullStr | Certain New Chebyshev and Grüss-Type Inequalities for Unified Fractional Integral Operators via an Extended Generalized Mittag-Leffler Function |
| title_full_unstemmed | Certain New Chebyshev and Grüss-Type Inequalities for Unified Fractional Integral Operators via an Extended Generalized Mittag-Leffler Function |
| title_short | Certain New Chebyshev and Grüss-Type Inequalities for Unified Fractional Integral Operators via an Extended Generalized Mittag-Leffler Function |
| title_sort | certain new chebyshev and gruss type inequalities for unified fractional integral operators via an extended generalized mittag leffler function |
| topic | Chebyshev integral inequality Grüss-type inequalities synchronous functions Mittag-Leffler function unified fractional integral operators |
| url | https://www.mdpi.com/2504-3110/6/4/182 |
| work_keys_str_mv | AT wenguiyang certainnewchebyshevandgrusstypeinequalitiesforunifiedfractionalintegraloperatorsviaanextendedgeneralizedmittaglefflerfunction |