An Extension of the Picard Theorem to Fractional Differential Equations with a Caputo-Fabrizio Derivative
In this paper, we consider fractional differential equations with the new fractional derivative involving a nonsingular kernel, namely, the Caputo-Fabrizio fractional derivative. Using a successive approximation method, we prove an extension of the Picard-Lindelöf existence and uniqueness theorem fo...
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| Format: | Article |
| Language: | English |
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Wiley
2021-01-01
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| Series: | Journal of Function Spaces |
| Online Access: | http://dx.doi.org/10.1155/2021/6624861 |
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| author | H. R. Marasi A. Soltani Joujehi H. Aydi |
| author_facet | H. R. Marasi A. Soltani Joujehi H. Aydi |
| author_sort | H. R. Marasi |
| collection | DOAJ |
| description | In this paper, we consider fractional differential equations with the new fractional derivative involving a nonsingular kernel, namely, the Caputo-Fabrizio fractional derivative. Using a successive approximation method, we prove an extension of the Picard-Lindelöf existence and uniqueness theorem for fractional differential equations with this derivative, which gives a set of conditions, under which a fractional initial value problem has a unique solution. |
| format | Article |
| id | doaj-art-8855d29843154555bce78db3c55b3253 |
| institution | Kabale University |
| issn | 2314-8896 2314-8888 |
| language | English |
| publishDate | 2021-01-01 |
| publisher | Wiley |
| record_format | Article |
| series | Journal of Function Spaces |
| spelling | doaj-art-8855d29843154555bce78db3c55b32532025-02-03T01:05:27ZengWileyJournal of Function Spaces2314-88962314-88882021-01-01202110.1155/2021/66248616624861An Extension of the Picard Theorem to Fractional Differential Equations with a Caputo-Fabrizio DerivativeH. R. Marasi0A. Soltani Joujehi1H. Aydi2Department of Applied Mathematics, Faculty of Mathematical Sciences, University of Tabriz, Tabriz, IranDepartment of Applied Mathematics, Faculty of Mathematical Sciences, University of Tabriz, Tabriz, IranUniversité de Sousse, Institut Supérieur d'Informatique et des Techniques de Communication, H. Sousse 4000, TunisiaIn this paper, we consider fractional differential equations with the new fractional derivative involving a nonsingular kernel, namely, the Caputo-Fabrizio fractional derivative. Using a successive approximation method, we prove an extension of the Picard-Lindelöf existence and uniqueness theorem for fractional differential equations with this derivative, which gives a set of conditions, under which a fractional initial value problem has a unique solution.http://dx.doi.org/10.1155/2021/6624861 |
| spellingShingle | H. R. Marasi A. Soltani Joujehi H. Aydi An Extension of the Picard Theorem to Fractional Differential Equations with a Caputo-Fabrizio Derivative Journal of Function Spaces |
| title | An Extension of the Picard Theorem to Fractional Differential Equations with a Caputo-Fabrizio Derivative |
| title_full | An Extension of the Picard Theorem to Fractional Differential Equations with a Caputo-Fabrizio Derivative |
| title_fullStr | An Extension of the Picard Theorem to Fractional Differential Equations with a Caputo-Fabrizio Derivative |
| title_full_unstemmed | An Extension of the Picard Theorem to Fractional Differential Equations with a Caputo-Fabrizio Derivative |
| title_short | An Extension of the Picard Theorem to Fractional Differential Equations with a Caputo-Fabrizio Derivative |
| title_sort | extension of the picard theorem to fractional differential equations with a caputo fabrizio derivative |
| url | http://dx.doi.org/10.1155/2021/6624861 |
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