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Mean value properties of fractional second order operators

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  • 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.
    Mathematics Subject Classification: Primary: 35H20, 35J60; Secondary: 35E05, 35J92.


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