Existence\u2013uniqueness and monotone iteration of positive solutions to nonlinear tempered fractional differential equation with p-Laplacian operator

Abstract

In this paper, without requiring the complete continuity of integral operators and the existence of upper–lower solutions, by means of the sum-type mixed monotone operator fixed point theorem based on the cone P_{h}, we investigate a kind of p-Laplacian differential equation Riemann–Stieltjes integral boundary value problem involving a tempered fractional derivative. Not only the existence and uniqueness of positive solutions are obtained, but also we can construct successively sequences for approximating the unique positive solution. As an application of our fundamental aims, we offer a realistic example to illustrate the effectiveness and practicability of the main results.