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Positive solutions for boundary value problem of nonlinear fractional differential equation. (English) Zbl 1079.34048

Summary: We investigate the existence and multiplicity of positive solutions to the boundary value problem

D 0+ α u(t)+ft , u ( t )=0,0<t<1,u(0)=u(1)=0,

where 1<α2 is a real number, D 0+ α is the standard Riemann-Liouville differentiation, and f:[0,1]×[0,)[0,) is continuous. By means of some fixed-point theorems in a cone, existence and multiplicity results positive solutions are obtained. The proofs are based upon the reduction of the problem considered to the equivalent Fredholm integral equation of second kind.

MSC:
34K05General theory of functional-differential equations
34B18Positive solutions of nonlinear boundary value problems for ODE
34B15Nonlinear boundary value problems for ODE
26A33Fractional derivatives and integrals (real functions)