The -Fractional Analogue for Gronwall-Type Inequality
We utilize -fractional Caputo initial value problems of order to derive a -analogue for Gronwall-type inequality. Some particular cases are derived where -Mittag-Leffler functions and -exponential type functions are used. An example is given to illustrate the validity of the derived inequality.
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| Main Authors: | , |
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| Format: | Article |
| Language: | English |
| Published: |
Wiley
2013-01-01
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| Series: | Journal of Function Spaces and Applications |
| Online Access: | http://dx.doi.org/10.1155/2013/543839 |
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| _version_ | 1832556629818605568 |
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| author | Thabet Abdeljawad Jehad O. Alzabut |
| author_facet | Thabet Abdeljawad Jehad O. Alzabut |
| author_sort | Thabet Abdeljawad |
| collection | DOAJ |
| description | We utilize -fractional Caputo initial value problems of order to derive a -analogue for Gronwall-type inequality. Some particular cases are derived where -Mittag-Leffler functions and -exponential type functions are used. An example is given to illustrate the validity of the derived inequality. |
| format | Article |
| id | doaj-art-ad890ccf6ec742b5ac6ac00c22503c67 |
| institution | Kabale University |
| issn | 0972-6802 1758-4965 |
| language | English |
| publishDate | 2013-01-01 |
| publisher | Wiley |
| record_format | Article |
| series | Journal of Function Spaces and Applications |
| spelling | doaj-art-ad890ccf6ec742b5ac6ac00c22503c672025-02-03T05:44:55ZengWileyJournal of Function Spaces and Applications0972-68021758-49652013-01-01201310.1155/2013/543839543839The -Fractional Analogue for Gronwall-Type InequalityThabet Abdeljawad0Jehad O. Alzabut1Department of Mathematics and Computer Science, Çankaya University, Ögretmenler Caddesi 14, Balgat, 06530 Ankara, TurkeyDepartment of Mathematics and Physical Sciences, Prince Sultan University, P.O. Box 66833, Riyadh 11586, Saudi ArabiaWe utilize -fractional Caputo initial value problems of order to derive a -analogue for Gronwall-type inequality. Some particular cases are derived where -Mittag-Leffler functions and -exponential type functions are used. An example is given to illustrate the validity of the derived inequality.http://dx.doi.org/10.1155/2013/543839 |
| spellingShingle | Thabet Abdeljawad Jehad O. Alzabut The -Fractional Analogue for Gronwall-Type Inequality Journal of Function Spaces and Applications |
| title | The -Fractional Analogue for Gronwall-Type Inequality |
| title_full | The -Fractional Analogue for Gronwall-Type Inequality |
| title_fullStr | The -Fractional Analogue for Gronwall-Type Inequality |
| title_full_unstemmed | The -Fractional Analogue for Gronwall-Type Inequality |
| title_short | The -Fractional Analogue for Gronwall-Type Inequality |
| title_sort | fractional analogue for gronwall type inequality |
| url | http://dx.doi.org/10.1155/2013/543839 |
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