DIFFERENtIAl & DIFFERENCE EqUAtIONS ANd APPlICAtIONS
DIFFERENtIAl & DIFFERENCE EqUAtIONS ANd APPlICAtIONS
DIFFERENtIAl & DIFFERENCE EqUAtIONS ANd APPlICAtIONS
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ON STRUCTURE OF FRACTIONAL SPACES GENERATED<br />
BY THE POSITIVE OPERATORS WITH THE NONLOCAL<br />
BOUNDARY CONDITIONS<br />
ALLABEREN ASHYRALYEV AND NERGIZ YAZ<br />
In the present paper, a structure of fractional spaces E α = E α (C[0,1],A x ) generated by the<br />
differential operator A x defined by the formula A x u =−a(x)(d 2 u/dx 2 )+δu with domain<br />
(A x ) ={u ∈ C (2) [0,1] : u(0) = u(μ), u ′ (0) = u ′ (1), 1/2 ≤ μ ≤ 1} is investigated. Here<br />
a(x) is a smooth function defined on the segment [0,1] and a(x) ≥ a>0, δ>0. It is established<br />
that for any 0
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