On weighted Atangana–Baleanu fractional operators

Mohammed Al-Refai

doi:10.1186/s13662-019-2471-z

On weighted Atangana–Baleanu fractional operators

Mohammed Al-Refai

Research output: Contribution to journal › Article › peer-review

71 Citations (Scopus)

Abstract

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.

Original language	English
Article number	3
Journal	Advances in Difference Equations
Volume	2020
Issue number	1
DOIs	https://doi.org/10.1186/s13662-019-2471-z
Publication status	Published - Dec 1 2020
Externally published	Yes

Keywords

Fractional derivatives with nonsingular kernels
Fractional differential equations
Weighted fractional derivatives

ASJC Scopus subject areas

Analysis
Algebra and Number Theory
Applied Mathematics

Access to Document

10.1186/s13662-019-2471-z

Cite this

@article{baf94e024ff14f6fa99a8154cfc13727,

title = "On weighted Atangana–Baleanu fractional operators",

abstract = "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.",

keywords = "Fractional derivatives with nonsingular kernels, Fractional differential equations, Weighted fractional derivatives",

author = "Mohammed Al-Refai",

note = "Publisher Copyright: {\textcopyright} 2019, The Author(s).",

year = "2020",

month = dec,

day = "1",

doi = "10.1186/s13662-019-2471-z",

language = "English",

volume = "2020",

journal = "Advances in Difference Equations",

issn = "1687-1839",

publisher = "Springer Publishing Company",

number = "1",

}

TY - JOUR

T1 - On weighted Atangana–Baleanu fractional operators

AU - Al-Refai, Mohammed

PY - 2020/12/1

Y1 - 2020/12/1

N2 - 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.

AB - 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.

KW - Fractional derivatives with nonsingular kernels

KW - Fractional differential equations

KW - Weighted fractional derivatives

UR - http://www.scopus.com/inward/record.url?scp=85077285982&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=85077285982&partnerID=8YFLogxK

U2 - 10.1186/s13662-019-2471-z

DO - 10.1186/s13662-019-2471-z

M3 - Article

AN - SCOPUS:85077285982

SN - 1687-1839

VL - 2020

JO - Advances in Difference Equations

JF - Advances in Difference Equations

IS - 1

M1 - 3

ER -

On weighted Atangana–Baleanu fractional operators

Abstract

Keywords

ASJC Scopus subject areas

Access to Document

Other files and links

Fingerprint

Cite this