Generalized fractional Stockwell transform and its associated pseudo-differential operator

Abstract

The novel fractional Stockwell transform is extended to the suitably defined Schwartz space and the generalized fractional Stockwell transform is introduced. The pseudo-differential operator associated with the fractional Stockwell transform is defined and it is proved to be continuous on the Schwartz space. Examples are illustrated for the generalized fractional Stockwell transform. The generalized convection-diffusion equation is solved using the fractional Stockwell transform.

Keywords:

• Fractional fourier transform
• fractional wavelet transform
• fractional Stockwell transform
• Schwartz space
• distributions
• pseudo-differential operator

2020 Mathematics Subject Classification:

•  42B10; 42F12; 47G30

Acknowledgments

The author would like to thank the editor and the anonymous reviewers for their constructive comments and valuable suggestions to improve the quality of the paper.

Disclosure statement

No potential conflict of interest was reported by the author(s).