On Novel Fractional Operators Involving the Multivariate Mittag–Leffler Function
The multivariate Mittag–Leffler function is introduced and used to establish fractional calculus operators. It is shown that the fractional derivative and integral operators are bounded. Some fundamental characteristics of the new fractional operators, such as the semi-group and inverse characterist...
| Main Authors: | , , , , , |
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| Format: | Article |
| Language: | English |
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MDPI AG
2022-10-01
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| Series: | Mathematics |
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| Online Access: | https://www.mdpi.com/2227-7390/10/21/3991 |
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| author | Muhammad Samraiz Ahsan Mehmood Saima Naheed Gauhar Rahman Artion Kashuri Kamsing Nonlaopon |
| author_facet | Muhammad Samraiz Ahsan Mehmood Saima Naheed Gauhar Rahman Artion Kashuri Kamsing Nonlaopon |
| author_sort | Muhammad Samraiz |
| collection | DOAJ |
| description | The multivariate Mittag–Leffler function is introduced and used to establish fractional calculus operators. It is shown that the fractional derivative and integral operators are bounded. Some fundamental characteristics of the new fractional operators, such as the semi-group and inverse characteristics, are studied. As special cases of these novel fractional operators, several fractional operators that are already well known in the literature are acquired. The generalized Laplace transform of these operators is evaluated. By involving the explored fractional operators, a kinetic differintegral equation is introduced, and its solution is obtained by using the Laplace transform. As a real-life problem, a growth model is developed and its graph is sketched. |
| first_indexed | 2024-03-09T18:52:53Z |
| format | Article |
| id | doaj.art-6d2a940f738b4fed9ee2fcc229c6df15 |
| institution | Directory Open Access Journal |
| issn | 2227-7390 |
| language | English |
| last_indexed | 2024-03-09T18:52:53Z |
| publishDate | 2022-10-01 |
| publisher | MDPI AG |
| record_format | Article |
| series | Mathematics |
| spelling | doaj.art-6d2a940f738b4fed9ee2fcc229c6df152023-11-24T05:43:14ZengMDPI AGMathematics2227-73902022-10-011021399110.3390/math10213991On Novel Fractional Operators Involving the Multivariate Mittag–Leffler FunctionMuhammad Samraiz0Ahsan Mehmood1Saima Naheed2Gauhar Rahman3Artion Kashuri4Kamsing Nonlaopon5Department of Mathematics, University of Sargodha, Sargodha 40100, PakistanDepartment of Mathematics, University of Sargodha, Sargodha 40100, PakistanDepartment of Mathematics, University of Sargodha, Sargodha 40100, PakistanDepartment of Mathematics and Statistics, Hazara University, Mansehra 21300, PakistanDepartment of Mathematics, Faculty of Technical and Natural Sciences, University Ismail Qemali, 9400 Vlora, AlbaniaDepartment of Mathematics, Khon Kaen University, Khon Kaen 40002, ThailandThe multivariate Mittag–Leffler function is introduced and used to establish fractional calculus operators. It is shown that the fractional derivative and integral operators are bounded. Some fundamental characteristics of the new fractional operators, such as the semi-group and inverse characteristics, are studied. As special cases of these novel fractional operators, several fractional operators that are already well known in the literature are acquired. The generalized Laplace transform of these operators is evaluated. By involving the explored fractional operators, a kinetic differintegral equation is introduced, and its solution is obtained by using the Laplace transform. As a real-life problem, a growth model is developed and its graph is sketched.https://www.mdpi.com/2227-7390/10/21/3991multivariate Mittag–Lefflerfractional integralfractional derivativegeneralized Laplace transform |
| spellingShingle | Muhammad Samraiz Ahsan Mehmood Saima Naheed Gauhar Rahman Artion Kashuri Kamsing Nonlaopon On Novel Fractional Operators Involving the Multivariate Mittag–Leffler Function Mathematics multivariate Mittag–Leffler fractional integral fractional derivative generalized Laplace transform |
| title | On Novel Fractional Operators Involving the Multivariate Mittag–Leffler Function |
| title_full | On Novel Fractional Operators Involving the Multivariate Mittag–Leffler Function |
| title_fullStr | On Novel Fractional Operators Involving the Multivariate Mittag–Leffler Function |
| title_full_unstemmed | On Novel Fractional Operators Involving the Multivariate Mittag–Leffler Function |
| title_short | On Novel Fractional Operators Involving the Multivariate Mittag–Leffler Function |
| title_sort | on novel fractional operators involving the multivariate mittag leffler function |
| topic | multivariate Mittag–Leffler fractional integral fractional derivative generalized Laplace transform |
| url | https://www.mdpi.com/2227-7390/10/21/3991 |
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