Existence of Mild Solutions to Nonlocal Fractional Cauchy Problems via Compactness
We obtain characterizations of compactness for resolvent families of operators and as applications we study the existence of mild solutions to nonlocal Cauchy problems for fractional derivatives in Banach spaces. We discuss here simultaneously the Caputo and Riemann-Liouville fractional derivatives...
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| Format: | Article |
| Language: | English |
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Wiley
2016-01-01
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| Series: | Abstract and Applied Analysis |
| Online Access: | http://dx.doi.org/10.1155/2016/4567092 |
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| _version_ | 1832563580814229504 |
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| author | Rodrigo Ponce |
| author_facet | Rodrigo Ponce |
| author_sort | Rodrigo Ponce |
| collection | DOAJ |
| description | We obtain characterizations of compactness for resolvent families of operators and as applications we study the existence of mild solutions to nonlocal Cauchy problems for fractional derivatives in Banach spaces. We discuss here simultaneously the Caputo and Riemann-Liouville fractional derivatives in the cases 0<α<1 and 1<α<2. |
| format | Article |
| id | doaj-art-940b7dd179f74405a6147341d111f5fe |
| institution | Kabale University |
| issn | 1085-3375 1687-0409 |
| language | English |
| publishDate | 2016-01-01 |
| publisher | Wiley |
| record_format | Article |
| series | Abstract and Applied Analysis |
| spelling | doaj-art-940b7dd179f74405a6147341d111f5fe2025-02-03T01:13:09ZengWileyAbstract and Applied Analysis1085-33751687-04092016-01-01201610.1155/2016/45670924567092Existence of Mild Solutions to Nonlocal Fractional Cauchy Problems via CompactnessRodrigo Ponce0Instituto de Matemática y Física, Universidad de Talca, Casilla 747, Talca, ChileWe obtain characterizations of compactness for resolvent families of operators and as applications we study the existence of mild solutions to nonlocal Cauchy problems for fractional derivatives in Banach spaces. We discuss here simultaneously the Caputo and Riemann-Liouville fractional derivatives in the cases 0<α<1 and 1<α<2.http://dx.doi.org/10.1155/2016/4567092 |
| spellingShingle | Rodrigo Ponce Existence of Mild Solutions to Nonlocal Fractional Cauchy Problems via Compactness Abstract and Applied Analysis |
| title | Existence of Mild Solutions to Nonlocal Fractional Cauchy Problems via Compactness |
| title_full | Existence of Mild Solutions to Nonlocal Fractional Cauchy Problems via Compactness |
| title_fullStr | Existence of Mild Solutions to Nonlocal Fractional Cauchy Problems via Compactness |
| title_full_unstemmed | Existence of Mild Solutions to Nonlocal Fractional Cauchy Problems via Compactness |
| title_short | Existence of Mild Solutions to Nonlocal Fractional Cauchy Problems via Compactness |
| title_sort | existence of mild solutions to nonlocal fractional cauchy problems via compactness |
| url | http://dx.doi.org/10.1155/2016/4567092 |
| work_keys_str_mv | AT rodrigoponce existenceofmildsolutionstononlocalfractionalcauchyproblemsviacompactness |