Existence of Multiple Positive Solutions for a General System of Fractional Differential Equations

摘要

In this paper, we study existence of multiple positive solutions of a coupled system of fractional differential equations {D_0~α+u(t) + Xa(t)f(v(t)) = 0, 0 < t < 1, {D_0~β+v(t) + Xb(t)g(u(t)) = 0, 0 < t < 1, subject to the two-point boundary conditions {u(1) = 0, u (0) = 0, u" (0) = 0,• • • , u~(n-2) (0) = 0, u~(n-1)(0) = 0, {v(1) = 0, v(0) = 0,v"(0) = 0,• • • v~(n-2)(0)=0,v(n-1)(0) = 0, where A>0, n— 1 < a,0 < n and D_0~α is the Caputo fractional derivative. By using Guo-Krasnosel'skii's fixed point theorem, we prove several existence results. We include some examples to show the applicability of our results.