Liu, Suli; Li, Yanchu; Li, Huilai Existence of solutions for a nonlinear fractional differential equation with boundary value conditions. (Chinese. English summary) Zbl 1340.34025 J. Jilin Univ., Sci. 53, No. 2, 194-198 (2015). Summary: We consider the nonlinear fractional differential equation \[ \begin{aligned} &{}^cD^\alpha_{0^+}u(t)=f(t,u(t),u'(t)) \text{ for a. e. }\;t\in (0,1),\\ &u(0)=u'(1)=u''(0)=0,\end{aligned} \] where \({}^cD^\alpha_{0^+}\) is the Caputo fractional derivative, \(2<\alpha\leqslant 3\) is a real number. We prove the existence of at least one solution of the boundary value problem using the Leray-Schauder continuation principle. MSC: 34A08 Fractional ordinary differential equations 34B15 Nonlinear boundary value problems for ordinary differential equations 47N20 Applications of operator theory to differential and integral equations Keywords:fractional differential equation; Carathéodory conditions; a priori estimate; Leray-Schauder continuation principle PDFBibTeX XMLCite \textit{S. Liu} et al., J. Jilin Univ., Sci. 53, No. 2, 194--198 (2015; Zbl 1340.34025) Full Text: DOI