Positive solutions of an initial value problem for nonlinear fractional differential equations (Q437640)

Summary: We investigate the existence and multiplicity of positive solutions for the nonlinear fractional differential equation initial value problem \(D^\alpha_{0+} u(t) + D^\beta_{0+} u(t) = f(t, u(t)), u(0) = 0\), \(0 < t < 1\), where \(0 < \beta < \alpha < 1\), \(D^\alpha_{0+}\) is the standard Riemann-Liouville differentiation and \(f : [0, 1] \times [0, \infty) \rightarrow [0, \infty)\) is continuous. By using some fixed-point results on cones, some existence and multiplicity results of positive solutions are obtained.