In this paper we introduce a method to define fractional operators using mean value operators. In particular we discuss a geometric approach in order to construct fractional operators. As a byproduct we define fractional linear operators in Carnot groups, moreover we adapt our technique to define some nonlinear fractional operators associated with the p−Laplace operators in Carnot groups.
Mean value properties of fractional second order operators
FERRARI, FAUSTO
2015
Abstract
In this paper we introduce a method to define fractional operators using mean value operators. In particular we discuss a geometric approach in order to construct fractional operators. As a byproduct we define fractional linear operators in Carnot groups, moreover we adapt our technique to define some nonlinear fractional operators associated with the p−Laplace operators in Carnot groups.File in questo prodotto:
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