Commutative property

Pure mathematics

Mathematics

Partial differential equation

Convergent series

Fractional calculus

Mathematical analysis

Power series

Differential equation

Applied mathematics

Ordinary differential equation

Advances in Difference Equations

In this paper, we define the weighted Atangana–Baleanu fractional operators of Caputo sense. We obtain the solution of a related linear fractional differential equation in a closed form, and use the result to define the weighted Atangana–Baleanu fractional integral. We then express the weighted Atangana–Baleanu fractional derivative in a convergent series of Riemann–Liouville fractional integrals, and establish commutative results of the weighted Atangana–Baleanu fractional operators.

On weighted Atangana–Baleanu fractional operators