Some fractional integral inequalities involving extended Mittag-Leffler function with applications
Integral inequalities and the Mittag-Leffler function play a crucial role in many branches of mathematics and applications, including fractional calculus, mathematical physics, and engineering. In this paper, we introduced an extended generalized Mittag-Leffler function that involved several well-kn...
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| Format: | Article |
| Language: | English |
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AIMS Press
2024-12-01
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| Series: | AIMS Mathematics |
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| Online Access: | https://www.aimspress.com/article/doi/10.3934/math.20241689 |
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| author | Sabir Hussain Rida Khaliq Sobia Rafeeq Azhar Ali Jongsuk Ro |
| author_facet | Sabir Hussain Rida Khaliq Sobia Rafeeq Azhar Ali Jongsuk Ro |
| author_sort | Sabir Hussain |
| collection | DOAJ |
| description | Integral inequalities and the Mittag-Leffler function play a crucial role in many branches of mathematics and applications, including fractional calculus, mathematical physics, and engineering. In this paper, we introduced an extended generalized Mittag-Leffler function that involved several well-known Mittag-Leffler functions as a special case. We also introduced an associated generalized fractional integral to obtain some estimates for fractional integral inequalities of the Hermite-Hadamard and Hermite-Hadamard-Fejér types. This article offered several analytical tools that will be useful to anyone working in this field. To demonstrate the veracity of our findings, we offered a few numerical and graphical examples. A few applications of modified Bessel functions and unitarily invariant norm of matrices were also given. |
| format | Article |
| id | doaj-art-5ef2ce85bc4c47deab416de9d92414c2 |
| institution | Kabale University |
| issn | 2473-6988 |
| language | English |
| publishDate | 2024-12-01 |
| publisher | AIMS Press |
| record_format | Article |
| series | AIMS Mathematics |
| spelling | doaj-art-5ef2ce85bc4c47deab416de9d92414c22025-01-23T07:53:25ZengAIMS PressAIMS Mathematics2473-69882024-12-01912355993562510.3934/math.20241689Some fractional integral inequalities involving extended Mittag-Leffler function with applicationsSabir Hussain0Rida Khaliq1Sobia Rafeeq2Azhar Ali3Jongsuk Ro4Department of Mathematics, University of Engineering and Technology, 54890, Lahore, PakistanDepartment of Mathematics, University of Engineering and Technology, 54890, Lahore, PakistanDepartment of Basic Sciences and Humanities (Mathematics), MNS University of Engineering and Technology, 60600, Multan, PakistanDepartment of Mathematics and Computer Science, Freie University Berlin, 14163, Berlin, GermanySchool of Electrical and Electronics Engineering, Chung-Ang University, Dongjak-gu, Seoul, 06974, Republic of KoreaIntegral inequalities and the Mittag-Leffler function play a crucial role in many branches of mathematics and applications, including fractional calculus, mathematical physics, and engineering. In this paper, we introduced an extended generalized Mittag-Leffler function that involved several well-known Mittag-Leffler functions as a special case. We also introduced an associated generalized fractional integral to obtain some estimates for fractional integral inequalities of the Hermite-Hadamard and Hermite-Hadamard-Fejér types. This article offered several analytical tools that will be useful to anyone working in this field. To demonstrate the veracity of our findings, we offered a few numerical and graphical examples. A few applications of modified Bessel functions and unitarily invariant norm of matrices were also given.https://www.aimspress.com/article/doi/10.3934/math.20241689mittag-leffler functions and generalizationshermite-hadamard type inequalitiesfractional integralsinequalities involving matricesmodified bessel functions |
| spellingShingle | Sabir Hussain Rida Khaliq Sobia Rafeeq Azhar Ali Jongsuk Ro Some fractional integral inequalities involving extended Mittag-Leffler function with applications AIMS Mathematics mittag-leffler functions and generalizations hermite-hadamard type inequalities fractional integrals inequalities involving matrices modified bessel functions |
| title | Some fractional integral inequalities involving extended Mittag-Leffler function with applications |
| title_full | Some fractional integral inequalities involving extended Mittag-Leffler function with applications |
| title_fullStr | Some fractional integral inequalities involving extended Mittag-Leffler function with applications |
| title_full_unstemmed | Some fractional integral inequalities involving extended Mittag-Leffler function with applications |
| title_short | Some fractional integral inequalities involving extended Mittag-Leffler function with applications |
| title_sort | some fractional integral inequalities involving extended mittag leffler function with applications |
| topic | mittag-leffler functions and generalizations hermite-hadamard type inequalities fractional integrals inequalities involving matrices modified bessel functions |
| url | https://www.aimspress.com/article/doi/10.3934/math.20241689 |
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