Existence of positive solutions of the boundary value problem for nonlinear fractional differential equations. (English) Zbl 1189.34014

Li, C. F.; Luo, X. N.; Zhou, Yong

Comput. Math. Appl. 59, No. 3, 1363-1375 (2010).

Summary: We are concerned with the nonlinear differential equation of fractional order \[ D^{\alpha}_{0+}u(t)+f(t,u(t))=0,~0<t<1,~1<\alpha\leq 2, \] where \(D^{\alpha}_{0+}\) is the standard Riemann-Liouville fractional derivative, subject to the boundary conditions \(u(0)=0\), \(D^{\beta}_{0+}u(1)=aD^{\beta}_{0+}u(\xi)\). We obtain the existence and multiplicity results of positive solutions by using some fixed point theorems.

MSC:

34A08	Fractional ordinary differential equations
26A33	Fractional derivatives and integrals
45J05	Integro-ordinary differential equations

Keywords:

Riemann-Liouville derivative; Carathéodory conditions; fractional differential equation; boundary value problem; positive solution

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