The Structure of Fractional Spaces Generated by a Two-Dimensional Difference Neutron Transport Operator and Its Applications

In this study, the structure of fractional spaces generated by the two-dimensional difference neutron transport operator Ar,h defined by formula $$\begin{aligned} A_{r,h}u^{r,h}=\left\{ \omega _{1}\frac{u_{m}^{n}-u_{m}^{n-1}}{r}+\omega _{2} \frac{u_{m}^{n-1}-u_{m-1}^{n-1}}{h}\right\} _{n,m=0,\pm 1,\pm 2,\ldots } \end{aligned}$$Ar,hur,h={ω1umn-umn-1r+ω2umn-1-um-1n-1h}n,m=0,±1,±2,… is investigated. The positivity of Ar,h in C(R(r,h)2) is established. The structure of fractional spaces generated by the operator Ar,h is studied. It is established that for any 0<α<1 the norms in the spaces Eα(C(R(r,h)2),Ar,h) and Cα(R(r,h)2) are equivalent. The positivity of the difference neutron transport operator in Hölder space Cα(R(r,h)2) is proved. © 2021, Springer Nature Switzerland AG.