The Method of almost convergence with operator of the form fractional order and applications

TL;DR

This paper surveys key concepts like almost convergence and fractional difference operators, then constructs new sequence spaces using these operators and characterizes matrix transformations for these spaces.

Contribution

It introduces new almost convergent spaces based on fractional order difference operators and provides their dual spaces and matrix transformation characterizations.

Findings

Constructed new sequence spaces with fractional difference operators

Computed dual spaces for these new sequence spaces

Characterized matrix transformations on these spaces

Abstract

The purpose of this paper is twofold. First, basic concepts such as Gamma function, almost convergence, fractional order difference operator and sequence spaces are given as a survey character. Thus, the current knowledge about those concepts are presented. Second, we construct the almost convergent spaces with fractional order difference operator and compute dual spaces which are help us in the characterization of matrix mappings. After we characterize to the matrix transformations, we give some examples.