Fractional Laplacian
In mathematics, the fractional Laplacian is an operator, which generalizes the notion of spatial derivatives to fractional powers. Definition. For formula_1 can be defined on functions formula_2 as a Fourier multiplier given by the formula where the Fourier transform formula_4 of a function formula_2 is given by More concretely, the fractional Laplacian can be written as a singular integral operator defined by Some authors prefer to adopt the convention of defining the fractional Laplacian of order s as formula_8 (as defined above), where now <math>0, so that the notion of order matches that of a (pseudo-)differential operator