Unique iterative positive solutions for a singular p-Laplacian fractional differential equation system with infinite-point boundary conditions

Abstract

By using the method of mixed monotone operator, a unique positive solution is obtained for a singular p-Laplacian boundary value system with infinite-point boundary conditions in this paper. Green’s function is derived and some useful properties of the Green’s function are obtained. Based upon these new properties and by using mixed monotone operator, the existence results of the positive solutions for the boundary value problem are established. Moreover, the unique positive solution that we obtained in this paper is dependent on λ, μ, and an iterative sequence and convergence rate, which are important for practical application, are given. An example is given to demonstrate the application of our main results.