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Zbl 1223.34107
Li, Xiaoyan; Liu, Song; Jiang, Wei
Positive solutions for boundary value problem of nonlinear fractional functional differential equations.
(English)
[J] Appl. Math. Comput. 217, No. 22, 9278-9285 (2011). ISSN 0096-3003

Summary: In this paper, we investigate the existence of positive solutions for the nonlinear Caputo fractional order functional differential equation $$D^\alpha_{0+}u(t)+a(t)f(u_t)=0,\quad 0<t<1,\ 1<\alpha\le 2,$$ where $D^\alpha_{0+}$ is the Caputo fractional order derivative, subject to the boundary conditions $$-au(t)+bu'(t)=\xi(t),\quad -\tau\le t\le 0,$$ $$cu(t)+du'(t)=\eta(t),\quad 1\le t\le 1+\beta,$$ we obtain the existence results of positive solutions by using some fixed point theorems.
MSC 2000:
*34K37
34K10 Boundary value problems for functional-differential equations

Keywords: Caputo derivative; fractional functional differential equation; boundary value problem; positive solution

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