On weighted Atangana–Baleanu fractional operators
Mohammed Al-Refai
Abstract
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.
Topics & Concepts
MathematicsFractional calculusOrdinary differential equationPartial differential equationConvergent seriesMathematical analysisApplied mathematicsCommutative propertyDifferential equationPure mathematicsPower seriesFractional Differential Equations SolutionsNonlinear Differential Equations AnalysisDifferential Equations and Boundary Problems