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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Format: | Article |
Language: | English |
Published: |
SpringerOpen
2020-01-01
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Series: | Advances in Difference Equations |
Subjects: | |
Online Access: | https://doi.org/10.1186/s13662-019-2471-z |
Summary: | 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. |
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ISSN: | 1687-1847 |