TY - JOUR
T1 - On weighted Atangana–Baleanu fractional operators
AU - Al-Refai, Mohammed
N1 - Funding Information:
The author express his sincere appreciation to the Research Affairs at Yarmouk University for their support.
Publisher Copyright:
© 2019, The Author(s).
PY - 2020/12/1
Y1 - 2020/12/1
N2 - 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.
AB - 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.
KW - Fractional derivatives with nonsingular kernels
KW - Fractional differential equations
KW - Weighted fractional derivatives
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U2 - 10.1186/s13662-019-2471-z
DO - 10.1186/s13662-019-2471-z
M3 - Article
AN - SCOPUS:85077285982
SN - 1687-1839
VL - 2020
JO - Advances in Difference Equations
JF - Advances in Difference Equations
IS - 1
M1 - 3
ER -