On Hilfer cotangent fractional derivative and a particular class of fractional problems-Reference-Cited by-同舟云学术

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

Published:2023 Issue:12 Volume:8 Page:28334-28352
ISSN:2473-6988
Container-title:AIMS Mathematics
language:
Short-container-title:MATH

Author:

Sadek Lakhlifa¹,Lazǎr Tania A²

Affiliation:

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

Abstract

<abstract><p>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.</p></abstract>

Publisher

American Institute of Mathematical Sciences (AIMS)

Subject

General Mathematics

Reference45 articles.

1. A. Atangana, E. F. D. Goufo, Cauchy problems with fractal-fractional operators and applications to groundwater dynamics, Fractals, 28 (2020), 2040043. https://doi.org/10.1142/S0218348X20400435

2. L. Debnath, Recent applications of fractional calculus to science and engineering, Int. J. Math. Math. Sci., 2003 (2003), 753601. https://doi.org/10.1155/S0161171203301486

3. R. Hilfer, Applications of fractional calculus in physics, Singapore: World Scientific, 2000. https://doi.org/10.1142/3779

4. A. A. Kilbas, H. M. Srivastava, J. J. Trujillo, Theory and applications of fractional differential equations, North-Holland Mathematics Studies, Vol. 204, Amsterdam: North-Holland, 2006.

5. R. L. Magin, Fractional calculus in bioengineering, Vol. 149, Redding: Begell House Publishers, 2006.

Cited by 9 articles. 订阅此论文施引文献订阅此论文施引文献，注册后可以免费订阅5篇论文的施引文献，订阅后可以查看论文全部施引文献

1. Introducing novel Θ-fractional operators: Advances in fractional calculus;Journal of King Saud University - Science;2024-10

2. On generalized $(k,\psi )$-Hilfer proportional fractional operator and its applications to the higher-order Cauchy problem;Boundary Value Problems;2024-07-03

3. Control theory for fractional differential Sylvester matrix equations with Caputo fractional derivative;Journal of Vibration and Control;2024-04-14

4. The Galerkin Bell method to solve the fractional optimal control problems with inequality constraints;Journal of Computational Science;2024-04

5. Controllability, observability, and stability of φ‐conformable fractional linear dynamical systems;Asian Journal of Control;2024-02-26