On the Theory of Fractional Calculus in the Pettis-Function Spaces
Throughout this paper, we outline some aspects of fractional calculus in Banach spaces. Some examples are demonstrated. In our investigations, the integrals and the derivatives are understood as Pettis integrals and the corresponding derivatives. Our results here extended all previous contributions...
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| Format: | Article |
| Language: | English |
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Hindawi Limited
2018-01-01
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| Series: | Journal of Function Spaces |
| Online Access: | http://dx.doi.org/10.1155/2018/8746148 |
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doaj-b5e9024fa789435fa81439e74d9127872020-11-24T22:45:59ZengHindawi LimitedJournal of Function Spaces2314-88962314-88882018-01-01201810.1155/2018/87461488746148On the Theory of Fractional Calculus in the Pettis-Function SpacesHussein A. H. Salem0Department of Mathematics and Computer Science, Faculty of Science, Alexandria University, Alexandria, EgyptThroughout this paper, we outline some aspects of fractional calculus in Banach spaces. Some examples are demonstrated. In our investigations, the integrals and the derivatives are understood as Pettis integrals and the corresponding derivatives. Our results here extended all previous contributions in this context and therefore are new. To encompass the full scope of our paper, we show that a weakly continuous solution of a fractional order integral equation, which is modeled off some fractional order boundary value problem (where the derivatives are taken in the usual definition of the Caputo fractional weak derivative), may not solve the problem.http://dx.doi.org/10.1155/2018/8746148 |
| collection |
DOAJ |
| language |
English |
| format |
Article |
| sources |
DOAJ |
| author |
Hussein A. H. Salem |
| spellingShingle |
Hussein A. H. Salem On the Theory of Fractional Calculus in the Pettis-Function Spaces Journal of Function Spaces |
| author_facet |
Hussein A. H. Salem |
| author_sort |
Hussein A. H. Salem |
| title |
On the Theory of Fractional Calculus in the Pettis-Function Spaces |
| title_short |
On the Theory of Fractional Calculus in the Pettis-Function Spaces |
| title_full |
On the Theory of Fractional Calculus in the Pettis-Function Spaces |
| title_fullStr |
On the Theory of Fractional Calculus in the Pettis-Function Spaces |
| title_full_unstemmed |
On the Theory of Fractional Calculus in the Pettis-Function Spaces |
| title_sort |
on the theory of fractional calculus in the pettis-function spaces |
| publisher |
Hindawi Limited |
| series |
Journal of Function Spaces |
| issn |
2314-8896 2314-8888 |
| publishDate |
2018-01-01 |
| description |
Throughout this paper, we outline some aspects of fractional calculus in Banach spaces. Some examples are demonstrated. In our investigations, the integrals and the derivatives are understood as Pettis integrals and the corresponding derivatives. Our results here extended all previous contributions in this context and therefore are new. To encompass the full scope of our paper, we show that a weakly continuous solution of a fractional order integral equation, which is modeled off some fractional order boundary value problem (where the derivatives are taken in the usual definition of the Caputo fractional weak derivative), may not solve the problem. |
| url |
http://dx.doi.org/10.1155/2018/8746148 |
| work_keys_str_mv |
AT husseinahsalem onthetheoryoffractionalcalculusinthepettisfunctionspaces |
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