On the existence of solution to a boundary value problem of fractional differential equation on the infinite interval

• DOI: 10.1186/s13661-015-0509-z
• Publication Date: 2015-12-29T09:35:36Z
• Authors: Chunfang Shen; Hui Zhou; Liu Yang
• Keywords: Interval (graph theory); Fractional Differential Equations; FOS: Political science; Norm (philosophy); 0211 other engineering and technologies; FOS: Law; 02 engineering and technology; Theory and Applications of Fractional Differential Equations; Mathematical analysis; Quantum mechanics; Engineering; Differential equation; FOS: Mathematics; Schauder fixed point theorem; Fixed-point theorem; Boundary value problem; Political science; Anomalous Diffusion Modeling and Analysis; Algebra and Number Theory; Applied Mathematics; Physics; Partial differential equation; Boundary Value Problems; Initial value problem; Control and Systems Engineering; Picard–Lindelöf theorem; Combinatorics; Modeling and Simulation; Physical Sciences; Analysis and Control of Distributed Parameter Systems; Nonlinear system; Law; Analysis; Mathematics; Ordinary differential equation

This work deals with a boundary value problem for nonlinear multi-point fractional differential equation on the infinite interval. By constructing proper function spaces and norm, we overcome difficulty following from noncompactness of $[0, \infty)$ . using Schauder fixed point theorem, show existence one solution suitable growth conditions imposed term.