A class of sequence spaces defined by $l$-fractional difference operator

TL;DR

This paper introduces a new class of sequence spaces based on a generalized fractional difference operator using the $l$-Pochhammer symbol, exploring their topological properties and duals.

Contribution

It generalizes the fractional difference operator with the $l$-Pochhammer symbol and defines new sequence spaces with studied topological features.

Findings

New $l$-fractional difference operator defined

Topological properties of the new spaces analyzed

Dual spaces characterized

Abstract

In this paper, we generalize the fractional order difference operator using $l$- Pochhammer symbol and define $l$- fractional difference operator. The $l$- fractional difference operator is further used to introduce a class of difference sequence spaces. Some topological properties and duals of the newly defined spaces are studied.