Existence of positive solutions for singular fractional differential equations with infinite-point boundary conditions

By Limin Guo, Lishan Liu, Yonghong Wu. 2016

91 citations recorded by the source corpus.

In this paper, we investigate the existence of at least three positive solutions to a singular boundary value problem of Caputo's fractional differential equations with a boundary condition involving values at infinite number of points. Firstly, we establish Green's function and its properties. Then, the existence of multiple positive solutions is obtained by Avery–Peterson's fixed point theorem. Finally, an example is given to demonstrate the application of our main results.

Subfields: Applied Mathematics, Modeling and Simulation, Numerical Analysis

View Paper: https://www.semanticscholar.org/paper/246e0aa2446b85d74364257465b9cc4692ac50c9

Citations in the corpus

• Stability and existence results for a class of nonlinear fractional differential equations with singularity (2018, unknown): “∗(u(t)) = 1 ∫ 0 β(t, s)φq ( 1 Γ(σ) s ∫ 0 (s − θ)σ−1[ (θ)ψ1(θ,u(θ))]dθ ) ds (25)”