The Borel-Pompieu formula involving proportional fractional $\psi$-Cauchy-Riemann operators

TL;DR

This paper extends the quaternionic Borel-Pompieu formula to proportional fractional $$-Cauchy-Riemann operators using Riemann-Liouville derivatives, broadening the mathematical framework for fractional calculus in quaternionic analysis.

Contribution

It introduces a novel analog of the Borel-Pompieu formula involving proportional fractional $$-Cauchy-Riemann operators with Riemann-Liouville derivatives.

Findings

Established a fractional quaternionic Borel-Pompieu formula.

Extended classical quaternionic analysis to fractional derivatives.

Provided mathematical tools for future research in fractional quaternionic analysis.

Abstract

We prove an analog of the quaternionic Borel-Pompieu formula in the sense of proportional fractional $\psi$-Cauchy-Riemann operators via Riemann-Liouville derivative with respect to another function.