Abstract
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.
Original language | English |
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Article number | 3 |
Journal | Advances in Difference Equations |
Volume | 2020 |
Issue number | 1 |
DOIs | |
Publication status | Published - Dec 1 2020 |
Externally published | Yes |
Keywords
- Fractional derivatives with nonsingular kernels
- Fractional differential equations
- Weighted fractional derivatives
ASJC Scopus subject areas
- Analysis
- Algebra and Number Theory
- Applied Mathematics