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Positive solutions for a class of singular fractional boundary value problems. (English) Zbl 1235.34010
Summary: We investigate the existence and uniqueness of positive solutions for the following singular fractional boundary value problem $$D^\alpha_{0^+}u(t)+f(t,u(t))=0,\ 0<t<1,\quad u(0)=u(1)=0,$$ where $1<\alpha\le 2, D^\alpha_{0^+}$ is the standard Riemann-Liouville differentiation and $f:(0,1 \times[0,\infty)\to[0,\infty)$ with $\lim_{t\to 0^+}f(t,-)= \infty$ (i.e., $f$ is singular at $t=0)$. Our analysis relies on a fixed point theorem in partially ordered sets.

34A08Fractional differential equations
34B18Positive solutions of nonlinear boundary value problems for ODE
34B16Singular nonlinear boundary value problems for ODE
47N20Applications of operator theory to differential and integral equations
Full Text: DOI
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