Positive solutions for fractional (p, q)-difference boundary value problems

In this paper, we investigate the boundary value problem of a class of fractional (p, q)-difference equations involving the Riemann-Liouville fractional derivative. Based on the generalization of Banach contraction principle, we obtain a sufficient condition for existence and uniqueness of solutions of the problem. By applying a fixed point theorem in cones, we establish a sufficient condition for the existence of at least one positive solution of the problem. As an application, some examples are presented to illustrate the main results.

Automated summary

This paper investigates the boundary value problem of a class of fractional (p, q)-difference equations involving the Riemann-Liouville fractional derivative. A sufficient condition for existence and uniqueness of solutions is obtained using the generalization of Banach contraction principle, while a sufficient condition for the existence of at least one positive solution is established by applying a fixed point theorem in cones. Several examples are presented to illustrate the main results.