A Bicomplex Proportional Fractional (ϑ,φ)-Weighted Cauchy–Riemann Operator Using Riemann–Liouville Derivatives with Respect to an Hyperbolic-Valued Function - José Oscar González-Cervantes; Juan Bory-Reyes; Juan Adrián Ramírez-Belman (Fractal and Fractional)
Based on the Riemann–Liouville derivatives with respect to functions taking values in the set of hyperbolic numbers, we consider a new bicomplex proportional fractional <semantics>(ϑ,φ)</semantics>-weighted Cauchy–Riemann operator, involving orthogonal bicomplex functions as weights, and its associated fractional Borel–Pompeiu formula is proved as the main result.