Approximate solutions of Atangana-Baleanu variable order fractional problems

Xiuying Li; Yang Gao; Boying Wu; Xiuying Li; Yang Gao; Boying Wu

doi:10.3934/math.2020151

AIMS Mathematics

2020, Volume 5, Issue 3: 2285-2294. doi: 10.3934/math.2020151

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Research article

Approximate solutions of Atangana-Baleanu variable order fractional problems

1.
School of Mathematics and Statistics, Changshu Institute of Technology, Changshu, Jiangsu 215500, PR China
2.
School of Mathematics and Statistics, University of South Florida, Tampa, Florida 33620, USA
3.
School of Mathematical Sciences, Harbin Institute of Technology, Harbin, Heilongjiang 150001, PR China

Received: 20 December 2019 Accepted: 27 February 2020 Published: 02 March 2020
MSC : 65L60, 65R20

The main aim of this paper is to propose a new approach for Atangana-Baleanu variable order fractional problems. We introduce a new reproducing kernel function with polynomial form. The advantage is that its fractional derivatives can be calculated explicitly. Based on this kernel function, a new collocation technique is developed for variable order fractional problems in the Atangana-Baleanu fractional sense. To show the accuracy and effectiveness of our approach, we provide three numerical experiments.
- reproducing kernel method,
- Atangana-Baleanu derivative,
- variable fractional order,
- collocation method
Citation: Xiuying Li, Yang Gao, Boying Wu. Approximate solutions of Atangana-Baleanu variable order fractional problems[J]. AIMS Mathematics, 2020, 5(3): 2285-2294. doi: 10.3934/math.2020151

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Abstract

The main aim of this paper is to propose a new approach for Atangana-Baleanu variable order fractional problems. We introduce a new reproducing kernel function with polynomial form. The advantage is that its fractional derivatives can be calculated explicitly. Based on this kernel function, a new collocation technique is developed for variable order fractional problems in the Atangana-Baleanu fractional sense. To show the accuracy and effectiveness of our approach, we provide three numerical experiments.

References

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