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 (φp)−1= φq, 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.
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机译：在本文中，我们研究了与P-拉普型操作员分数微分方程的正解的存在：等式，0 =φq，1 / p + 1 / q = 1和等式是标准的riemann-liouville差异化。有价值的是指出非线性F可以在 t = 0,1 或 u = 0 处是奇异的。通过在锥体上使用固定点定理和上下解决方案方法，获得了正溶液的存在。
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