Neutral functional sequential differential equations with Caputo fractional derivative on time scales
Abstract In this paper, we establish the existence and uniqueness of a solution for a class of initial value problems for implicit fractional differential equations with Caputo fractional derivative. The arguments are based upon the Banach contraction principle, the nonlinear alternative of Leray–Sc...
| Main Authors: | , , , |
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| Format: | Article |
| Language: | English |
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SpringerOpen
2022-03-01
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| Series: | Fixed Point Theory and Algorithms for Sciences and Engineering |
| Subjects: | |
| Online Access: | https://doi.org/10.1186/s13663-022-00716-9 |
| _version_ | 1818920593363304448 |
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| author | Jamal Eddine Lazreg Nadia Benkhettou Mouffak Benchohra Erdal Karapinar |
| author_facet | Jamal Eddine Lazreg Nadia Benkhettou Mouffak Benchohra Erdal Karapinar |
| author_sort | Jamal Eddine Lazreg |
| collection | DOAJ |
| description | Abstract In this paper, we establish the existence and uniqueness of a solution for a class of initial value problems for implicit fractional differential equations with Caputo fractional derivative. The arguments are based upon the Banach contraction principle, the nonlinear alternative of Leray–Schauder type and Krasnoselskii fixed point theorem. As applications, two examples are included to show the applicability of our results. |
| first_indexed | 2024-12-20T01:24:13Z |
| format | Article |
| id | doaj.art-00d84306ce144d25add6c516259c5e91 |
| institution | Directory Open Access Journal |
| issn | 2730-5422 |
| language | English |
| last_indexed | 2024-12-20T01:24:13Z |
| publishDate | 2022-03-01 |
| publisher | SpringerOpen |
| record_format | Article |
| series | Fixed Point Theory and Algorithms for Sciences and Engineering |
| spelling | doaj.art-00d84306ce144d25add6c516259c5e912022-12-21T19:58:17ZengSpringerOpenFixed Point Theory and Algorithms for Sciences and Engineering2730-54222022-03-012022111610.1186/s13663-022-00716-9Neutral functional sequential differential equations with Caputo fractional derivative on time scalesJamal Eddine Lazreg0Nadia Benkhettou1Mouffak Benchohra2Erdal Karapinar3Laboratory of Mathematics, Djillali Liabes University of Sidi Bel-AbbesLaboratory of Mathematics, Djillali Liabes University of Sidi Bel-AbbesLaboratory of Mathematics, Djillali Liabes University of Sidi Bel-AbbesDivision of Applied Mathematics, Thu Dau Mot UniversityAbstract In this paper, we establish the existence and uniqueness of a solution for a class of initial value problems for implicit fractional differential equations with Caputo fractional derivative. The arguments are based upon the Banach contraction principle, the nonlinear alternative of Leray–Schauder type and Krasnoselskii fixed point theorem. As applications, two examples are included to show the applicability of our results.https://doi.org/10.1186/s13663-022-00716-9Initial value problemCaputo’s fractional derivativeSequential neutral functional differential equationsFractional integralFixed pointExistence |
| spellingShingle | Jamal Eddine Lazreg Nadia Benkhettou Mouffak Benchohra Erdal Karapinar Neutral functional sequential differential equations with Caputo fractional derivative on time scales Fixed Point Theory and Algorithms for Sciences and Engineering Initial value problem Caputo’s fractional derivative Sequential neutral functional differential equations Fractional integral Fixed point Existence |
| title | Neutral functional sequential differential equations with Caputo fractional derivative on time scales |
| title_full | Neutral functional sequential differential equations with Caputo fractional derivative on time scales |
| title_fullStr | Neutral functional sequential differential equations with Caputo fractional derivative on time scales |
| title_full_unstemmed | Neutral functional sequential differential equations with Caputo fractional derivative on time scales |
| title_short | Neutral functional sequential differential equations with Caputo fractional derivative on time scales |
| title_sort | neutral functional sequential differential equations with caputo fractional derivative on time scales |
| topic | Initial value problem Caputo’s fractional derivative Sequential neutral functional differential equations Fractional integral Fixed point Existence |
| url | https://doi.org/10.1186/s13663-022-00716-9 |
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