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Positive solutions for boundary value problem of nonlinear fractional functional differential equations. (English) Zbl 1223.34107

Summary: In this paper, we investigate the existence of positive solutions for the nonlinear Caputo fractional order functional differential equation

D 0+ α u(t)+a(t)f(u t )=0,0<t<1,1<α2,

where D 0+ α is the Caputo fractional order derivative, subject to the boundary conditions

-au(t)+bu ' (t)=ξ(t),-τt0,
cu(t)+du ' (t)=η(t),1t1+β,

we obtain the existence results of positive solutions by using some fixed point theorems.

MSC:
34K37Functional-differential equations with fractional derivatives
34K10Boundary value problems for functional-differential equations
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