Compact operators on the sets of fractional difference sequences

TL;DR

This paper investigates the properties of operators on fractional difference sequence spaces, providing new estimates, characterizations of compact operators, and generalizing previous results in the field.

Contribution

It introduces new identities and estimates for operator norms and measures of noncompactness on fractional difference sequence spaces, extending existing literature.

Findings

Derived new estimates for operator norms.

Characterized classes of compact operators.

Provided more general results than previous studies.

Abstract

Fractional difference sequence spaces have been studied in the literature recently. In this work, some identities or estimates for the operator norms and the Hausdorff measures of noncompactness of certain operators on some difference sequence spaces of fractional orders are established. Some classes of compact operators on those spaces are characterized. The results of this work are more general and comprehensive then many other studies in literature.