On a New Modification of the Erdélyi–Kober Fractional Derivative
In this paper, we introduce a new Caputo-type modification of the Erdélyi–Kober fractional derivative. We pay attention to how to formulate representations of Erdélyi–Kober fractional integral and derivatives operators. Then, some properties of the new modification and relationships with other Erdél...
| Main Authors: | , |
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| Format: | Article |
| Language: | English |
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MDPI AG
2021-09-01
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| Series: | Fractal and Fractional |
| Subjects: | |
| Online Access: | https://www.mdpi.com/2504-3110/5/3/121 |
| _version_ | 1797519192870617088 |
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| author | Zaid Odibat Dumitru Baleanu |
| author_facet | Zaid Odibat Dumitru Baleanu |
| author_sort | Zaid Odibat |
| collection | DOAJ |
| description | In this paper, we introduce a new Caputo-type modification of the Erdélyi–Kober fractional derivative. We pay attention to how to formulate representations of Erdélyi–Kober fractional integral and derivatives operators. Then, some properties of the new modification and relationships with other Erdélyi–Kober fractional derivatives are derived. In addition, a numerical method is presented to deal with fractional differential equations involving the proposed Caputo-type Erdélyi–Kober fractional derivative. We hope the presented method will be widely applied to simulate such fractional models. |
| first_indexed | 2024-03-10T07:39:31Z |
| format | Article |
| id | doaj.art-4d025a2dd134452d9b9e76b2bf68dd2e |
| institution | Directory Open Access Journal |
| issn | 2504-3110 |
| language | English |
| last_indexed | 2024-03-10T07:39:31Z |
| publishDate | 2021-09-01 |
| publisher | MDPI AG |
| record_format | Article |
| series | Fractal and Fractional |
| spelling | doaj.art-4d025a2dd134452d9b9e76b2bf68dd2e2023-11-22T13:09:55ZengMDPI AGFractal and Fractional2504-31102021-09-015312110.3390/fractalfract5030121On a New Modification of the Erdélyi–Kober Fractional DerivativeZaid Odibat0Dumitru Baleanu1Department of Mathematics, Faculty of Science, Al-Balqa Applied University, Al-Salt 19117, JordanDepartment of Mathematics, Faculty of Arts and Sciences, Cankaya University, 06530 Ankara, TurkeyIn this paper, we introduce a new Caputo-type modification of the Erdélyi–Kober fractional derivative. We pay attention to how to formulate representations of Erdélyi–Kober fractional integral and derivatives operators. Then, some properties of the new modification and relationships with other Erdélyi–Kober fractional derivatives are derived. In addition, a numerical method is presented to deal with fractional differential equations involving the proposed Caputo-type Erdélyi–Kober fractional derivative. We hope the presented method will be widely applied to simulate such fractional models.https://www.mdpi.com/2504-3110/5/3/121fractional integrals and derivativesRiemann–Liouville fractional operatorCaputo fractional operatorErdélyi–Kober fractional operatorpredictor–corrector method |
| spellingShingle | Zaid Odibat Dumitru Baleanu On a New Modification of the Erdélyi–Kober Fractional Derivative Fractal and Fractional fractional integrals and derivatives Riemann–Liouville fractional operator Caputo fractional operator Erdélyi–Kober fractional operator predictor–corrector method |
| title | On a New Modification of the Erdélyi–Kober Fractional Derivative |
| title_full | On a New Modification of the Erdélyi–Kober Fractional Derivative |
| title_fullStr | On a New Modification of the Erdélyi–Kober Fractional Derivative |
| title_full_unstemmed | On a New Modification of the Erdélyi–Kober Fractional Derivative |
| title_short | On a New Modification of the Erdélyi–Kober Fractional Derivative |
| title_sort | on a new modification of the erdelyi kober fractional derivative |
| topic | fractional integrals and derivatives Riemann–Liouville fractional operator Caputo fractional operator Erdélyi–Kober fractional operator predictor–corrector method |
| url | https://www.mdpi.com/2504-3110/5/3/121 |
| work_keys_str_mv | AT zaidodibat onanewmodificationoftheerdelyikoberfractionalderivative AT dumitrubaleanu onanewmodificationoftheerdelyikoberfractionalderivative |