On slice regular fractal-fractional Dirichlet type spaces

TL;DR

This paper explores quaternionic slice regular function spaces influenced by a generalized fractal-fractional derivative, focusing on Banach spaces like Bergman and Dirichlet modules within this framework.

Contribution

It introduces new families of quaternionic slice regular function modules defined via a generalized fractal-fractional derivative, expanding the understanding of their structure and properties.

Findings

Defined new right modules of slice regular functions

Analyzed properties of Bergman and Dirichlet modules

Connected fractal-fractional derivatives with quaternionic function spaces

Abstract

In this paper, we study some families of right modules of quaternionic slice regular functions induced by a generalized fractal-fractional derivative with respect to a truncated quaternionic exponential function on slices. Important Banach spaces of slice regular functions, namely the Bergman and the Dirichlet modules, are two important elements of one of our families.