On Some Fractional order Binomial sequence spaces with infinite Matrices

TL;DR

This paper introduces new fractional order binomial difference sequence spaces using infinite matrices, exploring their topological properties, bases, and duals, thus expanding the mathematical framework of sequence space theory.

Contribution

It presents novel fractional order binomial difference sequence spaces and analyzes their topological properties, bases, and duals, which were not previously studied.

Findings

Defined new fractional order binomial difference sequence spaces

Analyzed their topological properties and Schauder bases

Determined their α-, β-, and γ-duals

Abstract

The main purpose of this article is to introduce some new binomial difference sequence spaces of fractional order ${\tilde{\alpha}} $ along with infinite matrices. Some topological properties of these spaces are considered along with the Schauder basis and ${\alpha} -,\beta -$ and $\gamma -$duals of the spaces.