**6. Conclusions**

Throughout the paper, fractional symmetric Hahn integral, Riemann–Liouville and Caputo fractional symmetric Hahn difference operators have been introduced. In addition, the properties of these fractional symmetric Hahn operators have been proven. This work might be able to used as a basis for related research, such as defining the Laplace transform for fractional symmetric Hanh calculus or investigating the fractional symmetric Hahn-convolution product and computing its fractional symmetric Hahn–Laplace transform. Finally, we hope to employ these properties to solve symmetric Hahn difference problems in future works.

**Author Contributions:** Conceptualization, N.P. and T.S.; Methodology, N.P. and T.S.; Validation, N.P. and T.S.; Formal Analysis, N.P. and T.S.; Investigation, N.P. and T.S.; Writing—Original Draft Preparation, N.P. and T.S.; Writing—Review & Editing, N.P. and T.S.; Funding Acquisition, N.P.

**Funding:** This research was funded by King Mongkut's University of Technology North Bangkok. Contract no. KMUTNB-61-KNOW-027.

**Acknowledgments:** The last author of this research was supported by Suan Dusit University.

**Conflicts of Interest:** The authors declare no conflicts of interest regarding the publication of this paper.
