Fractional spaces generated by the positive differential operator in the half-line R~+ and their applications

摘要

In this study, the following operator is considered. Here, δ > 0 is the sufficiently large number and a(x) is a continuous function defined on R~+ with 0 < s_1 ≤ a(x)≤s_2 <∞.We investigate the positivity of this operator in Banach space and the structure of the fractional spaces generated by this operator.