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Positive solutions of a fractional boundary value problem with a fractional derivative boundary condition

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  • In this paper, we apply Krasnosel'skii's cone expansion and compression fixed point theorem to show the existence of at least one positive solution to the nonlinear fractional boundary value problem $D^\alpha_{0^+} u + a(t)f(u)=0$, $0 < t < 1$, $1 < \alpha \le 2$, satisfying boundary conditions $u(0)=D^\beta_{0^+} u(1)=0$, $0\le\beta\le1$.
    Mathematics Subject Classification: Primary: 34B18, 26A33; Secondary: 34B15.


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