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

80 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

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10.1186/s13662-019-2471-z

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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

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DO - 10.1186/s13662-019-2471-z

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JO - Advances in Difference Equations

JF - Advances in Difference Equations

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M1 - 3

ER -

On weighted Atangana–Baleanu fractional operators

Abstract

Keywords

ASJC Scopus subject areas

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