Iterative unique positive solutions for singular p-Laplacian fractional differential equation system with several parameters

Abstract

© Vilnius University, 2018. By using the method of reducing the order of a derivative, the higher-order fractional differential equation is transformed into the lower-order fractional differential equation and combined with the mixed monotone operator, a unique positive solution is obtained in this paper for a singular p-Laplacian boundary value system with the Riemann-Stieltjes integral boundary conditions. This equation system is very wide because there are many parameters, which can be changeable in the equation system in this paper, and the nonlinearity is allowed to be singular in regard to not only the time variable but also the space variable. Moreover, the unique positive solution that we obtained in this paper is dependent on λ, and an iterative sequence and convergence rate are given, which are important for practical application. An example is given to demonstrate the application of our main results.