On weighted Atangana-Baleanu fractional operators

被引：52
|
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
  • [41] Approximate solutions of Atangana-Baleanu variable order fractional problems
    Li, Xiuying
    Gao, Yang
    Wu, Boying
    AIMS MATHEMATICS, 2020, 5 (03): : 2285 - 2294
  • [42] Modelling and simulation of a dynamical system with the Atangana-Baleanu fractional derivative
    Owolabi, Kolade M.
    EUROPEAN PHYSICAL JOURNAL PLUS, 2018, 133 (01):
  • [43] Modeling and analysis of the fractional HBV model with Atangana-Baleanu derivative
    Ullah, Saif
    Khan, Muhammad Altaf
    Farooq, Muhammad
    EUROPEAN PHYSICAL JOURNAL PLUS, 2018, 133 (08):
  • [44] Intrinsic Discontinuities in Solutions of Evolution Equations Involving Fractional Caputo-Fabrizio and Atangana-Baleanu Operators
    Angstmann, Christopher Nicholas
    Jacobs, Byron Alexander
    Henry, Bruce Ian
    Xu, Zhuang
    MATHEMATICS, 2020, 8 (11) : 1 - 16
  • [45] STABILITY OF NONLINEAR HYBRID FRACTIONAL DIFFERENTIAL EQUATION WITH ATANGANA-BALEANU OPERATOR
    Britto Jacob, S.
    George Maria, A.
    ADVANCES IN DIFFERENTIAL EQUATIONS AND CONTROL PROCESSES, 2022, 26 (01): : 1 - 19
  • [46] Stability analysis of Atangana-Baleanu fractional stochastic differential systems with impulses
    Dhayal, Rajesh
    Gomez-Aguilar, J. F.
    Torres-Jimenez, J.
    INTERNATIONAL JOURNAL OF SYSTEMS SCIENCE, 2022, 53 (16) : 3481 - 3495
  • [47] An analysis on approximate controllability of Atangana-Baleanu fractional semilinear control systems
    Williams, Williams Kavitha
    Vijayakumar, Velusamy
    Shukla, Anurag
    Nisar, Kottakkaran Sooppy
    INTERNATIONAL JOURNAL OF NONLINEAR SCIENCES AND NUMERICAL SIMULATION, 2023, 24 (07) : 2627 - 2638
  • [48] An epidemiological approach to insurgent population modeling with the Atangana-Baleanu fractional derivative
    Kolebaje, Olusola
    Popoola, Oyebola
    Khan, Muhammad Altaf
    Oyewande, Oluwole
    CHAOS SOLITONS & FRACTALS, 2020, 139
  • [49] Analysis of Silver Nanoparticles in Engine Oil: Atangana-Baleanu Fractional Model
    Murtaza, Saqib
    Ali, Farhad
    Sheikh, Nadeem Ahmad
    Khan, Ilyas
    Nisar, Kottakkaran Sooppy
    CMC-COMPUTERS MATERIALS & CONTINUA, 2021, 67 (03): : 2915 - 2932
  • [50] NUMERICAL ANALYSIS OF COUPLED FRACTIONAL DIFFERENTIAL EQUATIONS WITH ATANGANA-BALEANU FRACTIONAL DERIVATIVE
    Koca, Ilknur
    DISCRETE AND CONTINUOUS DYNAMICAL SYSTEMS-SERIES S, 2019, 12 (03): : 475 - 486
12345