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.
Highlights
The Hahn difference operator, one type of quantum difference operator, has been studied by many reseachers
Hahn [4] is the first researcher who introduced the Hahn difference operator Dq,ω based on the forward difference operator and the Jackson q-difference operator where
There are other works related to the Hahn difference operator such as the study of Hahn quantum variational calculus [7,8,9], and the existence and uniqueness results for the initial value problems [10,11,12]
Summary
The Hahn difference operator, one type of quantum difference operator, has been studied by many reseachers. There are other works related to the Hahn difference operator such as the study of Hahn quantum variational calculus [7,8,9], and the existence and uniqueness results for the initial value problems [10,11,12]. The boundary value problems for fractional Hahn difference equations were subsequently studied by many researchers (see [16,17,18,19]). The fractional symmetric Hahn difference operators of the Riemann–Liouville and Caputo types. We propose the fractional symmetric Hahn difference operators of the Riemann–Liouville and Caputo types and their properties in Sections 4 and 5, respectively
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