Fractional Cesàro Matrix and its Associated Sequence Space

In this research, we introduce a new fractional Cesàro matrix and investigate the topological properties of the sequence space associated with this matrix.We also introduce a fractional Gamma matrix aswell and obtain some factorizations for the Hilbert operator based on Cesàro and Gamma matrices. The results of these factorizations are two new inequalities one ofwhich is a generalized version of thewell-known Hilbert’s inequality. There are also some challenging problems that authors share at the end of the manuscript and invite the researcher for trying to solve them.