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

A bicomplex proportional fractional $(\vartheta,\varphi)-$weighted  Cauchy-Riemann operator using Riemann-Liouville derivatives with respect to  an hyperbolic-valued function