On weighted Atangana-Baleanu fractional operators

被引：44
|
作者：
Al-Refai, Mohammed [1 ]
机构：
[1] Yarmouk Univ, Dept Math, Irbid, Jordan
来源：
ADVANCES IN DIFFERENCE EQUATIONS | 2020年 / 2020卷 / 01期
关键词：
Weighted fractional derivatives; Fractional derivatives with nonsingular kernels; Fractional differential equations; EQUATIONS;
D O I：
10.1186/s13662-019-2471-z
中图分类号：
O29 [应用数学];
学科分类号：
070104 ;
摘要：
In this paper, we define the weighted Atangana-Baleanu fractional operators of Caputo sense. We obtain the solution of a related linear fractional differential equation in a closed form, and use the result to define the weighted Atangana-Baleanu fractional integral. We then express the weighted Atangana-Baleanu fractional derivative in a convergent series of Riemann-Liouville fractional integrals, and establish commutative results of the weighted Atangana-Baleanu fractional operators.
引用
收藏
页数：11
相关论文
共 50 条
  • [1] MODIFIED ATANGANA-BALEANU FRACTIONAL DIFFERENTIAL OPERATORS
    Ibrahim, Rabha W.
    Baleanu, Dumitru
    [J]. PROCEEDINGS OF THE INSTITUTE OF MATHEMATICS AND MECHANICS, 2022, 48 : 56 - 67
  • [2] On weighted Atangana–Baleanu fractional operators
    Mohammed Al-Refai
    [J]. Advances in Difference Equations, 2020
  • [3] A bibliometric analysis of Atangana-Baleanu operators in fractional calculus
    Templeton, Alexander
    [J]. ALEXANDRIA ENGINEERING JOURNAL, 2020, 59 (04) : 2733 - 2738
  • [4] Modelling the spread of Ebola virus with Atangana-Baleanu fractional operators
    Koca, Ilknur
    [J]. EUROPEAN PHYSICAL JOURNAL PLUS, 2018, 133 (03):
  • [5] Modelling the spread of Ebola virus with Atangana-Baleanu fractional operators
    Ilknur Koca
    [J]. The European Physical Journal Plus, 133
  • [6] Existence Results for Langevin Equation Involving Atangana-Baleanu Fractional Operators
    Baleanu, Dumitru
    Darzi, Rahmat
    Agheli, Bahram
    [J]. MATHEMATICS, 2020, 8 (03)
  • [7] Applications of the Atangana-Baleanu Fractional Integral Operator
    Lupas, Alina Alb
    Catas, Adriana
    [J]. SYMMETRY-BASEL, 2022, 14 (03):
  • [8] Some novel inequalities involving Atangana-Baleanu fractional integral operators and applications
    Vivas-Cortez, Miguel
    Awan, Muhammad Uzair
    Rafique, Sehrish
    Javed, Muhammad Zakria
    Kashuri, Artion
    [J]. AIMS MATHEMATICS, 2022, 7 (07): : 12203 - 12226
  • [9] FRACTIONAL INTEGRAL INEQUALITIES FOR PREINVEX FUNCTIONS VIA ATANGANA-BALEANU INTEGRAL OPERATORS
    Karaoglan, Ali
    Set, Erhan
    Akdemir, Ahmet Ocak
    Ozdemir, M. Emin
    [J]. MISKOLC MATHEMATICAL NOTES, 2024, 25 (01) : 329 - 347
  • [10] Fractional Integral Inequalities via Atangana-Baleanu Operators for Convex and Concave Functions
    Akdemir, Ahmet Ocak
    Karaoglan, Ali
    Ragusa, Maria Alessandra
    Set, Erhan
    [J]. JOURNAL OF FUNCTION SPACES, 2021, 2021
12345