Approximate solutions of Atangana-Baleanu variable order fractional problems

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.

Keywords

• reproducing kernel method
• atangana-baleanu derivative
• variable fractional order
• collocation method