A bicomplex $(\vartheta,\varphi)-$weighted fractional Borel-Pompeiu type formula

TL;DR

This paper develops a fractional bicomplex weighted Borel-Pompeiu formula using hyperbolic orthogonal bicomplex functions and Riemann-Liouville fractional calculus, extending integral formulas in bicomplex analysis.

Contribution

It introduces a new fractional bicomplex Borel-Pompeiu formula with weighted Cauchy-Riemann operators and hyperbolic orthogonal bicomplex functions, advancing fractional and bicomplex analysis.

Findings

Established a fractional bicomplex Borel-Pompeiu formula

Incorporated hyperbolic orthogonal bicomplex weights

Extended classical integral formulas to fractional bicomplex context

Abstract

The purpose of this paper is to establish a Borel-Pompeiu type formula induced from a fractional bicomplex $(\vartheta,\varphi)-$weighted Cauchy-Riemann operator, where the weights are two hyperbolic orthogonal bicomplex functions and the fractionality is understand in the Riemann-Liouville sense.