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Zbl 1244.34009
Zhang, Xinguang; Han, Yuefeng
Existence and uniqueness of positive solutions for higher order nonlocal fractional differential equations.
(English)
[J] Appl. Math. Lett. 25, No. 3, 555-560 (2012). ISSN 0893-9659

Summary: We are concerned with the existence and uniqueness of positive solutions for the following singular nonlinear $(n-1,1)$ conjugate-type fractional differential equation with a nonlocal term $$\cases D^\alpha_{0+}x(t)+f(t,x(t))=0,\ 0<t<1,\ n-1<\alpha\le n,\\ x^{(k)}(0) =0,\ 0\le k\le n-2,\ x(1)=\int^1_0x(s)dA(s),\endcases$$ where $\alpha \ge 2$, $D^\alpha_{0+}$ is the standard Riemann-Liouville derivative, $A$ is a function of bounded variation and $\int^1_0u(s)dA(s)$ denotes the Riemann-Stieltjes integral of $u$ with respect to $A$, $dA$ can be a signed measure.
MSC 2000:
*34A08
47N20 Appl. of operator theory to differential and integral equations
34B18 Positive solutions of nonlinear boundary value problems

Keywords: monotone iterative technique; fractional differential equation; existence and uniqueness; positive solution

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