In this paper we deal with two nonlocal operators, that are both well known and widely studied in the literature in connection with elliptic problems of fractional type. Precisely, for a fixed s ∈ (0, 1) we consider the integral definition of the fractional Laplacian given by (−∆)u(x) := c(n, s) 2 ∫ Rn 2u(x)− u(x+ y)− u(x− y) |y|n+2s dy , x ∈ R n , where c(n, s) is a positive normalizing consta...

The aim of this work is to introduce a novel concept, Riesz–Dunkl fractional derivatives, within the context Dunkl-type operators. A particularly noteworthy revelation that when specific parameter κ equals zero, derivative smoothly reduces both well-known Riesz and second-order derivative. Furthermore, we new concept: Sobolev space. This space defined characterized using versatile framework Dun...