Approximate solutions of Atangana-Baleanu variable order fractional problems

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 co...

Full description

Saved in:
Bibliographic Details
Published inAIMS mathematics Vol. 5; no. 3; pp. 2285 - 2294
Main Authors Li, Xiuying, Gao, Yang, Wu, Boying
Format Journal Article
LanguageEnglish
Published AIMS Press 01.01.2020
Subjects
atangana-baleanu derivative
collocation method
reproducing kernel method
variable fractional order
Online AccessGet full text
ISSN2473-6988
2473-6988
DOI10.3934/math.2020151

Cover

More Information
Summary: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.
ISSN:2473-6988
2473-6988
DOI:10.3934/math.2020151