Æ
/
℄
℄
/
Æ
℄
/ /
℄
Æ
℄
℄℄
, , .
,
.
, :
. , ,
.
Banach , , , Schauder ,
.
:
, , .
− Dvx(t) = f(t, x(t), Dγ x(t)), 0 < t < 1,
xi(0) = 0, 0 ≤ i ≤ n − 2, ()
Dγx(1) = aDγx(η), 1 ≤γ≤ n − 2
v
℄
, D Riemann-Liouville , n − 1 < v ≤ n, 0 ≤
v−γ−2
i ≤ n − 2, 1 ≤γ≤ n − 2, 0 < a ≤ 1, η∈(0, 1), aη≤ 1 −γ, v −γ− 1 ≥ 0,
f : [0, 1] × [0, +∞) × R →[0, +∞)
. Schauder ,
℄
, () .
℄
Dγx(t) + q(t)f(t, x(t)) = 0, 0 < t < 1,
()
′′′(n−2) ′′
x(0) = x (0) = x (0) = · · · = x (0) = 0, x (1) = ξx (η),
γγ−1
D Riemann-Liouville , n − 1 < γ≤ n, n ≥ 3, 0 < 1 −ξη<
1, 0 < η< 1.
f : [0, 1] × [0, +∞) →[0, +∞) .
i
℄
() .
cDαx(t) = f(t, x(t), (χx)(t)), 0 < t < 1, 1 < α≤ 2,
1 ()
x x g x , x′ q x s ds
(0) = 0 + ( ) (1) = ( ( ))
Z0
c
℄
, D Caputo , x0 ∈ R,
1
(χx)(t) = γ(t, s)x(s)ds, ()
Z
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