Ntouyas, Sotiris K.; Wang, Guotao; Zhang, Lihong Positive solutions of arbitrary order nonlinear fractional differential equations with advanced arguments. (English) Zbl 1235.34209 Opusc. Math. 31, No. 3, 433-442 (2011). This paper deals with the existence and uniqueness of positive solutions to arbitrary order nonlinear fractional differential equations with advanced arguments \[ D^\alpha_0 u(t)+ a(t)(u(\theta(t)))= 0, \;0<t<1,\;n-1<\alpha\leq n \] satisfying \[ u^{(i)} (0)=0,\;i=0,1,2,\ldots, n-2,\quad [ D_0^\beta u(t)]_{t=1} =0,\;1\leq \beta\leq n-2, \] where \(n>3\) (\(n\in \mathbb{N}\)), \(D^\alpha_0\) is the standard Riemann-Liouville fractional derivative of order \(\alpha\), \(f: [0, \infty) \to [0, \infty) \) and \(\theta : (0, 1) \to (0, 1]\) are continuous functions.The proof uses the Banach contraction principle and the well-known Guo-Krasnosel’skii fixed point theorem. Reviewer: Gisèle M. Mophou (Pointe-à-Pitre) Cited in 15 Documents MSC: 34K37 Functional-differential equations with fractional derivatives 34K17 Transformation and reduction of functional-differential equations and systems, normal forms 34K10 Boundary value problems for functional-differential equations 47N20 Applications of operator theory to differential and integral equations Keywords:positive solution; advanced arguments; fractional differential equations; superlinear condition; uniqueness PDFBibTeX XMLCite \textit{S. K. Ntouyas} et al., Opusc. Math. 31, No. 3, 433--442 (2011; Zbl 1235.34209) Full Text: DOI