On fractional Hahn calculus

Abstract

In this paper, the new concepts of Hahn difference operators are introduced. The properties of fractional Hahn calculus in the sense of a forward Hahn difference operator are introduced and developed.

On fractional $(p,q)$-calculus

“…Agarwal [45] and Al-Salam [46] introduced fractional q-difference calculus, while Díaz and Osler [47] studied fractional difference calculus. Recently, Brikshavana and Sitthiwirattham [48] introduced fractional Hahn difference calculus. In addition, Patanarapeelert and Sitthiwirattham [49] discussed fractional symmetric Hahn difference calculus.…”

A generalization of Minkowski’s inequality by Hahn integral operator

“…In this paper, we use Hahn FIO [13] for the integrable functions to produce Minkowski's integral inequalities. Our results are more general and applicable than the classical case.…”

“…We divide the paper in three main sections. This section is for literature review and includes some useful information about the Hahn calculus from [13]. Here, we highlight some relevant definitions from the available literature.…”

Some results on quantum Hahn integral inequalities

“…The Hahn difference operator is a successful tool for constructing families of orthogonal polynomials and investigating some approximation problems (cf. [3][4][5][6]). For some recent results to boundary value problems for Hahn difference operators, we refer to papers [7][8][9][10] and the references cited therein.…”