On quaternionic analysis and a certain generalized fractal-fractional $\psi$-Fueter operator

TL;DR

This paper introduces a novel fractional-fractal $ ext{-}Fueter$ operator in quaternionic analysis, combining fractional and fractal derivatives, and establishes fundamental integral formulas related to it.

Contribution

It presents the first formulation of a fractional-fractal $ ext{-}Fueter$ operator in quaternionic analysis, extending classical operators with fractal and fractional calculus concepts.

Findings

Defined the fractional-fractal $ ext{-}Fueter$ operator in quaternionic context

Derived Stokes and Borel-Pompeiu formulas for the new operator

Bridged fractional calculus, fractal measures, and quaternionic analysis

Abstract

This paper introduce a fractional-fractal $\psi$-Fueter operator in the quaternionic context inspired in the concepts of proportional fractional derivative and Hausdorff derivative of a function with respect to a fractal measure. Moreover, we establish the corresponding Stokes and Borel-Pompeiu formulas associated to this generalized fractional-fractal $\psi$-Fueter operator.