On Slice Regular Fractal–Fractional Dirichlet‐Type Spaces

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.