On abstract Cauchy problems in the frame of a generalized Caputo type derivative
In this paper, we consider a class of abstract Cauchy problems in the framework of a generalized Caputo type fractional. We discuss the existence and uniqueness of mild solutions to such a class of fractional differential equations by using properties found in the related fractional calculus, the th...
| Main Authors: | , , , , |
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| Format: | Article |
| Language: | English |
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ATNAA
2023-03-01
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| Series: | Advances in the Theory of Nonlinear Analysis and its Applications |
| Subjects: | |
| Online Access: | https://atnaea.org/index.php/journal/article/view/1/8 |
| _version_ | 1797257776183902208 |
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| author | Soumia Bourchi Fahd Jarad Yassine Adjabi Thabet Abdeljawad Ibrahim Mahariq |
| author_facet | Soumia Bourchi Fahd Jarad Yassine Adjabi Thabet Abdeljawad Ibrahim Mahariq |
| author_sort | Soumia Bourchi |
| collection | DOAJ |
| description | In this paper, we consider a class of abstract Cauchy problems in the framework of a generalized Caputo type fractional. We discuss the existence and uniqueness of mild solutions to such a class of fractional differential equations by using properties found in the related fractional calculus, the theory of uniformly continuous semigroups of operators and the fixed point theorem. Moreover, we discuss the continuous dependence on parameters and Ulam stability of the mild solutions. At the end of this paper, we bring forth some examples to endorse the obtained results |
| first_indexed | 2024-04-24T22:43:01Z |
| format | Article |
| id | doaj.art-cc37f891693e48c282e13c713e0ccb6e |
| institution | Directory Open Access Journal |
| issn | 2587-2648 |
| language | English |
| last_indexed | 2024-04-24T22:43:01Z |
| publishDate | 2023-03-01 |
| publisher | ATNAA |
| record_format | Article |
| series | Advances in the Theory of Nonlinear Analysis and its Applications |
| spelling | doaj.art-cc37f891693e48c282e13c713e0ccb6e2024-03-18T20:07:31ZengATNAAAdvances in the Theory of Nonlinear Analysis and its Applications2587-26482023-03-017112810.31197/atnaa.1147950On abstract Cauchy problems in the frame of a generalized Caputo type derivativeSoumia Bourchi0Fahd Jarad1Yassine Adjabi2Thabet Abdeljawad3Ibrahim Mahariq4Department of Mathematics, Faculty of Sciences, University of M'hamed Bougara, Boumerdes, AlgeriaDepartment of Mathematics, Faculty of Arts and Sciences, Çankaya University, Ankara, 06790, Turkey Department of Mathematics, Faculty of Sciences, University of M'hamed Bougara, Boumerdes, AlgeriaDepartment of Mathematics and Sciences, Prince Sultan University, P.O. Box66833, Riyadh, 11586,KSACollege of Engineering and Technology, American University of the Middle East ,KuwaitIn this paper, we consider a class of abstract Cauchy problems in the framework of a generalized Caputo type fractional. We discuss the existence and uniqueness of mild solutions to such a class of fractional differential equations by using properties found in the related fractional calculus, the theory of uniformly continuous semigroups of operators and the fixed point theorem. Moreover, we discuss the continuous dependence on parameters and Ulam stability of the mild solutions. At the end of this paper, we bring forth some examples to endorse the obtained resultshttps://atnaea.org/index.php/journal/article/view/1/8caputo type generalized fractional operatorsabstract cauchy problemexistenceuniquenesscontinuous dependence on parametersstabilityuniformly continuous semigroupsfixed point theoremsmittag-leffler type function |
| spellingShingle | Soumia Bourchi Fahd Jarad Yassine Adjabi Thabet Abdeljawad Ibrahim Mahariq On abstract Cauchy problems in the frame of a generalized Caputo type derivative Advances in the Theory of Nonlinear Analysis and its Applications caputo type generalized fractional operators abstract cauchy problem existence uniqueness continuous dependence on parameters stability uniformly continuous semigroups fixed point theorems mittag-leffler type function |
| title | On abstract Cauchy problems in the frame of a generalized Caputo type derivative |
| title_full | On abstract Cauchy problems in the frame of a generalized Caputo type derivative |
| title_fullStr | On abstract Cauchy problems in the frame of a generalized Caputo type derivative |
| title_full_unstemmed | On abstract Cauchy problems in the frame of a generalized Caputo type derivative |
| title_short | On abstract Cauchy problems in the frame of a generalized Caputo type derivative |
| title_sort | on abstract cauchy problems in the frame of a generalized caputo type derivative |
| topic | caputo type generalized fractional operators abstract cauchy problem existence uniqueness continuous dependence on parameters stability uniformly continuous semigroups fixed point theorems mittag-leffler type function |
| url | https://atnaea.org/index.php/journal/article/view/1/8 |
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