Existence of positive solutions for boundary value problem of fractional differential equation with p-Laplacian operator

In this paper, we investigate the existence of positive solutions of fractional differential equations with p- Laplacian operator: equation, 0 < t < 1, u(0)= u′(0)= u′(1)= 0, equation, 1 < γ ≤2, 2 < α ≤, equation where (φ
p
)
⁻¹
= φ
q
, 1/p + 1/q= 1 and equation is the standard Riemann-Liouville differentiation. It is valuable to point out that the nonlinearity f can be singular at
^{t= 0, 1}
or
^{u= 0}
. By the use of fixed point theorem on cone and the upper and lower solutions method, the existence of positive solutions is obtained.