On Hilfer cotangent fractional derivative and a particular class of fractional problems

Lakhlifa Sadek; Tania A Lazǎr; Lakhlifa Sadek; Tania A Lazǎr

doi:10.3934/math.20231450

AIMS Mathematics

2023, Volume 8, Issue 12: 28334-28352. doi: 10.3934/math.20231450

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Research article

On Hilfer cotangent fractional derivative and a particular class of fractional problems

Lakhlifa Sadek ¹,
Tania A Lazǎr ^{2
,
,}

1.
Faculty of Sciences and Technology, BP 34. Ajdir 32003 Al-Hoceima, Abdelmalek Essaadi University, Morocco
2.
Department of Mathematics, Technical University of Cluj-Napoca, 400114, Cluj Napoca, Romania

Received: 05 August 2023 Revised: 19 September 2023 Accepted: 21 September 2023 Published: 18 October 2023
MSC : 26A33, 34A12, 34A43, 34D20

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.
- cotangent fractional derivative,
- fixed point theorems,
- cotangent Volterra integral equation,
- Hilfer cotangent fractional derivative,
- existence
Citation: Lakhlifa Sadek, Tania A Lazǎr. On Hilfer cotangent fractional derivative and a particular class of fractional problems[J]. AIMS Mathematics, 2023, 8(12): 28334-28352. doi: 10.3934/math.20231450

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Abstract

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.

References

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