Iterative unique positive solutions for a new class of nonlinear singular higher order fractional differential equations with mixed-type boundary value conditions

In this paper, we consider a new class of singular nonlinear higher order fractional boundary value problems supplemented with sum of Riemann-Stieltjes integral type and nonlocal infinite-point discrete type boundary conditions. The fractional derivative of different orders is involved in the nonlinear terms and boundary conditions, and the nonlinear terms are allowed to be singular in regard to not only time variable but also space variables. A unique positive solution is established by using the fixed point theorem of mixed monotone operator. In addition, some significant properties of the unique solution depending on the parameter lambda are stated. In the end, two examples are worked out to illustrate our main results.