On weighted Atangana–Baleanu fractional operators

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 weig...

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Main Author: Mohammed Al-Refai
Format: Article
Language:English
Published: SpringerOpen 2020-01-01
Series:Advances in Difference Equations
Subjects:
Weighted fractional derivatives
Fractional derivatives with nonsingular kernels
Fractional differential equations
Online Access:https://doi.org/10.1186/s13662-019-2471-z
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spelling doaj-c52c663694854179b7bcbf3406912f9d2021-01-03T12:17:35ZengSpringerOpenAdvances in Difference Equations1687-18472020-01-012020111110.1186/s13662-019-2471-zOn weighted Atangana–Baleanu fractional operatorsMohammed Al-Refai0Department of Mathematics, Yarmouk UniversityAbstract 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.https://doi.org/10.1186/s13662-019-2471-zWeighted fractional derivativesFractional derivatives with nonsingular kernelsFractional differential equations
collection DOAJ
language English
format Article
sources DOAJ
author Mohammed Al-Refai
spellingShingle Mohammed Al-Refai
On weighted Atangana–Baleanu fractional operators
Advances in Difference Equations
Weighted fractional derivatives
Fractional derivatives with nonsingular kernels
Fractional differential equations
author_facet Mohammed Al-Refai
author_sort Mohammed Al-Refai
title On weighted Atangana–Baleanu fractional operators
title_short On weighted Atangana–Baleanu fractional operators
title_full On weighted Atangana–Baleanu fractional operators
title_fullStr On weighted Atangana–Baleanu fractional operators
title_full_unstemmed On weighted Atangana–Baleanu fractional operators
title_sort on weighted atangana–baleanu fractional operators
publisher SpringerOpen
series Advances in Difference Equations
issn 1687-1847
publishDate 2020-01-01
description 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.
topic Weighted fractional derivatives
Fractional derivatives with nonsingular kernels
Fractional differential equations
url https://doi.org/10.1186/s13662-019-2471-z
work_keys_str_mv AT mohammedalrefai onweightedatanganabaleanufractionaloperators
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