| Summary: | In this paper the existence of unique positive solutions for system of (p, q, r)-Lapalacian Sturm-Liouville type
two-point fractional order boundary vaue problems,
CDα
0+
φp(u(t))
+ f
t, u(t), v(t), w(t)
= 0, 0 < t < 1,
CD
β
0+
φq(v(t))
+ g
t, v(t), w(t), u(t)
= 0, 0 < t < 1,
CD
γ
0+
φr(w(t))
+ h
t, w(t), u(t), v(t)
= 0, 0 < t < 1,
a1(φpu)(0) − b1(φpu)
0
(0) = 0, c1(φpu)(1) + d1(φpu)
0
(1) = 0,
a2(φqv)(0) − b2(φqv)
0
(0) = 0, c2(φqv)(1) + d2(φqv)
0
(1) = 0,
a3(φrw)(0) − b3(φrw)
0
(0) = 0, c3(φrw)(1) + d3(φrw)
0
(1) = 0,
where 1 < α, β, γ ≤ 2, φ`(τ) = |τ|
`−2τ, ` ∈ (1, ∞),
CD?
0+ is a Caputo fractional derivatives of order
? ∈ {α, β, γ} and ai
, bi
, ci
, di
, i = 1, 2, 3 are positive constants, is established by an application of n-fixed
point theorem of ternary operators on partially ordered metric spaces
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