  Based on the Riemann-Liouville derivatives with respect to functions taking
values in the set of hyperbolic numbers, we consider a novel bicomplex
proportional fractional $(\vartheta,\varphi)-$weighted Cauchy-Riemann operator,
involving weights hyperbolic orthogonal bicomplex functions. This operator is
defined for the first time here, and its associated fractional Borel-Pompeiu
formula is proved as the main result.
