A fractional Borel-Pompeiu type formula and a related fractional $\psi -$Fueter operator with respect to a vector-valued function

In this paper we combine the fractional $\psi -$hyperholomorphic function theory with the fractional calculus with respect to another function. As a main result, a fractional Borel-Pompeiu type formula related to a fractional $\psi -$Fueter operator with respect to a vector-valued function, is proved.