On the solvability and approximate solution of a one-dimensional singular problem for a p-Laplacian fractional differential equation

•Existence and uniqueness of positive solutions to auxiliary nonsingular FBVPs.•Solvability of p-Laplacian singular FBVP and the interval where its solution exists.•Iterative scheme for solving p-Laplacian singular FBVP and its convergence. In this paper, using the monotone iterative technique, we discuss a new approximate method for solving multi-point boundary value problems of p-Laplacian fractional differential equations with singularities, which are of great importance in the fluid dynamics field. To do this, first, a sequence of auxiliary problems that release the nonlinear source terms contained in the equations from the singularities is set up, and the uniqueness and existence of their positive solutions are established. Next, we show the relative compactness of the sequence of unique solutions to these auxiliary problems to prove the solvability of our given problem. And we present some sufficient conditions to construct a sequence of approximate solutions that converges to an exact solution of our problem. Finally, we give two numerical examples to demonstrate our main results.