Mean value properties of fractional second order operators (Q2347689)

In this paper, the author defines fractional operators by using mean value operators. Furthermore, a geometric approach is also used to define new fractional operators associated with nonlinear local operators. In particular, fractional linear operators in Carnot groups and some nonlinear fractional operators associated with the \(p\)-Laplace operators in Carnot groups are also defined using this new approach and the results obtained are proved and discussed.