October 2, 2025

On Slice Regular Fractal–Fractional Dirichlet‐Type Spaces

Key Points

The study focuses on slice regular functions associated with a fractal-fractional derivative.
Key findings include the examination of Bergman and Dirichlet modules within Banach spaces.
A generalized fractal-fractional derivative is observed to affect quaternionic functions significantly.
Exploration of these modules may expand mathematical frameworks involving quaternionic analysis.

Abstract

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.

On Slice Regular Fractal–Fractional Dirichlet‐Type Spaces

Key Points

Abstract

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