On Hilfer cotangent fractional derivative and a particular class of fractional problems
In this work, a novel Hilfer cotangent fractional derivative is presented. This derivative combines the characteristics of the Riemann-Liouville cotangent fractional derivative and the Caputo cotangent fractional derivative. The essential properties of the newly introduced derivative are discussed....
| Main Authors: | , |
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| Format: | Article |
| Language: | English |
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AIMS Press
2023-10-01
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| Series: | AIMS Mathematics |
| Subjects: | |
| Online Access: | https://www.aimspress.com/article/doi/10.3934/math.20231450?viewType=HTML |
| _version_ | 1797644932750508032 |
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| author | Lakhlifa Sadek Tania A Lazǎr |
| author_facet | Lakhlifa Sadek Tania A Lazǎr |
| author_sort | Lakhlifa Sadek |
| collection | DOAJ |
| description | In this work, a novel Hilfer cotangent fractional derivative is presented. This derivative combines the characteristics of the Riemann-Liouville cotangent fractional derivative and the Caputo cotangent fractional derivative. The essential properties of the newly introduced derivative are discussed. By utilizing this derivative, a nonlinear fractional differential problem with a nonlocal initial condition is investigated, and its equivalence to a cotangent Volterra integral equation is demonstrated. The uniqueness and existence of solutions are established by employing fixed-point theorems. Additionally, two illustrative examples are provided to illustrate the obtained results. |
| first_indexed | 2024-03-11T14:38:34Z |
| format | Article |
| id | doaj.art-f1c1c2dfcdc24325955955a86a6204a7 |
| institution | Directory Open Access Journal |
| issn | 2473-6988 |
| language | English |
| last_indexed | 2024-03-11T14:38:34Z |
| publishDate | 2023-10-01 |
| publisher | AIMS Press |
| record_format | Article |
| series | AIMS Mathematics |
| spelling | doaj.art-f1c1c2dfcdc24325955955a86a6204a72023-10-31T01:49:22ZengAIMS PressAIMS Mathematics2473-69882023-10-01812283342835210.3934/math.20231450On Hilfer cotangent fractional derivative and a particular class of fractional problemsLakhlifa Sadek0Tania A Lazǎr 11. Faculty of Sciences and Technology, BP 34. Ajdir 32003 Al-Hoceima, Abdelmalek Essaadi University, Morocco2. Department of Mathematics, Technical University of Cluj-Napoca, 400114, Cluj Napoca, RomaniaIn this work, a novel Hilfer cotangent fractional derivative is presented. This derivative combines the characteristics of the Riemann-Liouville cotangent fractional derivative and the Caputo cotangent fractional derivative. The essential properties of the newly introduced derivative are discussed. By utilizing this derivative, a nonlinear fractional differential problem with a nonlocal initial condition is investigated, and its equivalence to a cotangent Volterra integral equation is demonstrated. The uniqueness and existence of solutions are established by employing fixed-point theorems. Additionally, two illustrative examples are provided to illustrate the obtained results.https://www.aimspress.com/article/doi/10.3934/math.20231450?viewType=HTMLcotangent fractional derivativefixed point theoremscotangent volterra integral equationhilfer cotangent fractional derivativeexistence |
| spellingShingle | Lakhlifa Sadek Tania A Lazǎr On Hilfer cotangent fractional derivative and a particular class of fractional problems AIMS Mathematics cotangent fractional derivative fixed point theorems cotangent volterra integral equation hilfer cotangent fractional derivative existence |
| title | On Hilfer cotangent fractional derivative and a particular class of fractional problems |
| title_full | On Hilfer cotangent fractional derivative and a particular class of fractional problems |
| title_fullStr | On Hilfer cotangent fractional derivative and a particular class of fractional problems |
| title_full_unstemmed | On Hilfer cotangent fractional derivative and a particular class of fractional problems |
| title_short | On Hilfer cotangent fractional derivative and a particular class of fractional problems |
| title_sort | on hilfer cotangent fractional derivative and a particular class of fractional problems |
| topic | cotangent fractional derivative fixed point theorems cotangent volterra integral equation hilfer cotangent fractional derivative existence |
| url | https://www.aimspress.com/article/doi/10.3934/math.20231450?viewType=HTML |
| work_keys_str_mv | AT lakhlifasadek onhilfercotangentfractionalderivativeandaparticularclassoffractionalproblems AT taniaalazar onhilfercotangentfractionalderivativeandaparticularclassoffractionalproblems |