reproducing kernel method, Atangana-Baleanu derivative, variable fractional order, collocation method
Digital Object Identifier (DOI)
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.
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Citation / Publisher Attribution
AIMS Mathematics, v. 5, issue 3, p. 2285-2294
Scholar Commons Citation
Li, Xiuying; Gao, Yang; and Wu, Boying, "Approximate Solutions of Atangana-Baleanu Variable Order Fractional Problems" (2020). Mathematics and Statistics Faculty Publications. 65.