Bai, Chuanzhi Triple positive solutions for a boundary value problem of nonlinear fractional differential equation. (English) Zbl 1183.34005 Electron. J. Qual. Theory Differ. Equ. 2008, Paper No. 24, 10 p. (2008). Summary: We investigate the existence of three positive solutions for the nonlinear fractional boundary value problem \[ D_{0+}^{\alpha} u(t) + a(t)f(t,u(t), u''(t))=0,\quad 0 < t < 1, \quad 3 < \alpha \leq 4, \]\[ u(0) = u'(0) = u''(0)= u''(1)=0 , \]where \(D_{0+}^{\alpha}\) is the standard Riemann-Liouville fractional derivative. The method involves applications of a new fixed-point theorem due to Bai and Ge. The interesting point lies in the fact that the nonlinear term is allowed to depend on the second order derivative \(u''\). Cited in 22 Documents MSC: 34A08 Fractional ordinary differential equations 34B18 Positive solutions to nonlinear boundary value problems for ordinary differential equations 47N20 Applications of operator theory to differential and integral equations Keywords:fractional derivative; boundary value problem; positive solution; fixed point theorem PDF BibTeX XML Cite \textit{C. Bai}, Electron. J. Qual. Theory Differ. Equ. 2008, Paper No. 24, 10 p. (2008; Zbl 1183.34005) Full Text: DOI EuDML EMIS