In this paper, we discuss the existence of positive solutions of a coupled system of p-laplacian fractional differential equations with integral boundary conditions. In this paper, we show some necessary deﬁnitions and lemmas, with doubling measure and in (quasi-)Banach function spaces. We find that the properties of Banach function spaces and the condition are used to get the conclusion, which is just the same as the conditions of the estimate of the functions in Theorem 1.1. Particularly, the condition could be seen as a separation condition in combining the given lemmas, we obtain important properties of Green's function associated with the fractional BVP. Thus, by Theorem 3.2, the FBVP has no positive solution. According to the properties of Green's function, by using Guo-Krasnosel' skii fixed point theorem on cones, we prove the existence, uniqueness, multiplicity results, and nonexistence of positive solutions for fractional boundary value problems. Finally, an example is provided to illustrate our main result.
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