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

Abstract

This paper introduce a fractal ψ-Fueter operator in the quaternionic context inspired in the concepts of proportional derivative and Hausdorff derivative (fractal derivative) of a function with respect to a fractal measure. Moreover, we establish the corresponding Stokes and Borel- Pompeiu formulas associated to this generalized fractal ψ-Fueter operator with respect to a vector valued function induced by truncated exponential functions.