×

Existence of solutions for a nonlinear fractional differential equation with boundary value conditions. (Chinese. English summary) Zbl 1340.34025

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
PDFBibTeX XMLCite
Full Text: DOI