Two-dimensional fractional shearlet transforms in $$L^2({\mathbb {R}}^2)$$

Abstract

The aim of this study is to introduce a convolution-based two-dimensional fractional shearlet transform in the context of fractional time-frequency analysis. The preliminary analysis encompasses the derivation of fundamental properties of the novel integral transform including the orthogonality relation, inversion formula, and the range theorem. To extend the scope of the study, the cone adapted variant of the two-dimensional fractional shearlet transform is also studied in detail. Nevertheless, several coherent examples are presented to facilitate a sound illustration of the concepts.