Structure of Fractional Spaces Generated by the Difference Operator and Its Applications

In the present paper, the positivity of the second order of approximation of the difference operator approximates the second-order differential operator with nonlocal conditions is established. The equivalence of norms of these fractional spaces generated by this operator and Hölder spaces is proved. In applications, the stability of difference schemes for the approximate solution of the boundary value problem for elliptic differential equations is provided. © 2017 Taylor & Francis.