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Zbl 1185.34008
Yuan, Chengjun; Jiang, Daqing; Xu, Xiaojie
Singular positone and semipositone boundary value problems of nonlinear fractional differential equations. (English)
[J] Math. Probl. Eng. 2009, Article ID 535209, 17 p. (2009). ISSN 1024-123X; ISSN 1563-5147/e

Summary: We present some new existence results for the singular positone and semipositone nonlinear fractional boundary value problem $${\bold D}_0^\alpha u(t)=\mu a(t)f(t,u(t)), \quad 0<t<1,$$ $$u(0)=u(1)=u'(0)=u'(1)=0,$$ where $\mu>0$, $a$, and $f$ are continuous, $\alpha\in (3,4]$ is a real number, and ${\bold D}_{0+}^\alpha$ is Riemann-Liouville fractional derivative. The nonlinearity may be singular in its dependent variable. Two examples are given to illustrate the main results.

MSC 2000:: *34A08
34B15 Nonlinear boundary value problems of ODE
34B16 Singular nonlinear boundary value problems
34B18 Positive solutions of nonlinear boundary value problems

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