*Article* **On Fractional Symmetric Hahn Calculus**

#### **Nichaphat Patanarapeelert 1 and Thanin Sitthiwirattham 2,\***


Received: 14 August 2019; Accepted: 17 September 2019; Published: 20 September 2019

**Abstract:** In this paper, we study fractional symmetric Hahn difference calculus. The new idea of the symmetric Hahn difference operator, the fractional symmetric Hahn integral, and the fractional symmetric Hahn operators of Riemann–Liouville and Caputo types are presented. In addition, we formulate some fundamental properties based on these fractional symmetric Hahn operators.

**Keywords:** fractional symmetric Hahn integral; fractional symmetric Hahn difference operator

**JEL Classification:** 39A10; 39A13; 39A70
