Research article

Approximate solutions of Atangana-Baleanu variable order fractional problems

  • 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.

    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

    Related Papers:

  • 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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