Descriptive analysis of new model of unbounded 3x3 operator matrix with application

In the present paper, we are interested to develop some spectral properties of new model of unbounded block 3x3 of operator matrix with non diagonal domain, named one sided block 3x3 of operator matrix. Some new hypotheses are invested assuring a new approach to find a fine description of the spectrum, the resolvent expression as well as some essential spectra of such new matrix model independently of the knowledge of the union of some essential spectra of its diagonal operators entries. Our developed results extending some known results from I. Marzouk et al. (from Georgian Math. J., https://doi.org/10.1515/gmj-2023-2071 (2023)) to the case of one sided block 3x3 of operator matrix form. Physical model of neutron transport equation with one partly elastic diagonal collision operator is stated to exam the validity of our theoretical framework.