Zhang, Shuqin2021-07-152021-07-152006-03-21Zhang, S. (2006). Positive solutions for boundary-value problems of nonlinear fractional differential equations. <i>Electronic Journal of Differential Equations, 2006</i>(36), pp. 1-12.1072-6691https://hdl.handle.net/10877/13909In this paper, we consider the existence and multiplicity of positive solutions for the nonlinear fractional differential equation boundary-value problem Dα0 + u(t) = ƒ(t, u(t)), 0 < t < 1 u(0) + u′(0) = 0, u(1) + u′(1) = 0 where 1 < α ≤ 2 is a real number, and Dα0+ is the Caputo's fractional derivative, and ƒ : [0, 1] x [0, +∞) → [0, +∞) is continuous. By means of a fixed-point theorem on cones, some existence and multiplicity results of positive solutions are obtained.Text12 pages1 file (.pdf)enAttribution 4.0 InternationalCaputo's fractional derivativeFractional differential equationBoundary-value problemPositive solutionFractional Green's functionFixed-point theoremArticleThis work is licensed under a Creative Commons Attribution 4.0 International License.