More properties of the proportional fractional integrals and derivatives of a function with respect to another function
Abstract In this article, we present some new properties of the fractional proportional derivatives of a function with respect to a certain function. We use a modified Laplace transform to find the relation between the derivatives in the Riemann–Liouville setting and the one in Caputo. In addition,...
| Main Authors: | , , , |
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| Format: | Article |
| Language: | English |
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SpringerOpen
2020-06-01
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| Series: | Advances in Difference Equations |
| Subjects: | |
| Online Access: | http://link.springer.com/article/10.1186/s13662-020-02767-x |
| _version_ | 1818696079654256640 |
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| author | Fahd Jarad Thabet Abdeljawad Saima Rashid Zakia Hammouch |
| author_facet | Fahd Jarad Thabet Abdeljawad Saima Rashid Zakia Hammouch |
| author_sort | Fahd Jarad |
| collection | DOAJ |
| description | Abstract In this article, we present some new properties of the fractional proportional derivatives of a function with respect to a certain function. We use a modified Laplace transform to find the relation between the derivatives in the Riemann–Liouville setting and the one in Caputo. In addition, we provide an integration by parts formulas related to the considered operators. |
| first_indexed | 2024-12-17T13:55:40Z |
| format | Article |
| id | doaj.art-4b62a192d34b45f1ab8779d98626a125 |
| institution | Directory Open Access Journal |
| issn | 1687-1847 |
| language | English |
| last_indexed | 2024-12-17T13:55:40Z |
| publishDate | 2020-06-01 |
| publisher | SpringerOpen |
| record_format | Article |
| series | Advances in Difference Equations |
| spelling | doaj.art-4b62a192d34b45f1ab8779d98626a1252022-12-21T21:45:56ZengSpringerOpenAdvances in Difference Equations1687-18472020-06-012020111610.1186/s13662-020-02767-xMore properties of the proportional fractional integrals and derivatives of a function with respect to another functionFahd Jarad0Thabet Abdeljawad1Saima Rashid2Zakia Hammouch3Department of Mathematics, Çankaya UniversityDepartment of Mathematics and General Sciences, Prince Sultan UniversityDepartment of Mathematics, Government College UniversityEquipe E3MI, Department of Mathematics, FST Errachidia, University Moulay IsmailAbstract In this article, we present some new properties of the fractional proportional derivatives of a function with respect to a certain function. We use a modified Laplace transform to find the relation between the derivatives in the Riemann–Liouville setting and the one in Caputo. In addition, we provide an integration by parts formulas related to the considered operators.http://link.springer.com/article/10.1186/s13662-020-02767-xGeneral proportional integralsGeneral proportional derivativesGeneral Caputo proportional derivative |
| spellingShingle | Fahd Jarad Thabet Abdeljawad Saima Rashid Zakia Hammouch More properties of the proportional fractional integrals and derivatives of a function with respect to another function Advances in Difference Equations General proportional integrals General proportional derivatives General Caputo proportional derivative |
| title | More properties of the proportional fractional integrals and derivatives of a function with respect to another function |
| title_full | More properties of the proportional fractional integrals and derivatives of a function with respect to another function |
| title_fullStr | More properties of the proportional fractional integrals and derivatives of a function with respect to another function |
| title_full_unstemmed | More properties of the proportional fractional integrals and derivatives of a function with respect to another function |
| title_short | More properties of the proportional fractional integrals and derivatives of a function with respect to another function |
| title_sort | more properties of the proportional fractional integrals and derivatives of a function with respect to another function |
| topic | General proportional integrals General proportional derivatives General Caputo proportional derivative |
| url | http://link.springer.com/article/10.1186/s13662-020-02767-x |
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