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Existence of positive solutions of the boundary value problem for nonlinear fractional differential equations. (English) Zbl 1189.34014

Summary: We are concerned with the nonlinear differential equation of fractional order

D 0+ α u(t)+f(t,u(t))=0,0<t<1,1<α2,

where D 0+ α is the standard Riemann-Liouville fractional derivative, subject to the boundary conditions u(0)=0, D 0+ β u(1)=aD 0+ β u(ξ). We obtain the existence and multiplicity results of positive solutions by using some fixed point theorems.

MSC:
34A08Fractional differential equations
26A33Fractional derivatives and integrals (real functions)
45J05Integro-ordinary differential equations
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