Unique positive solutions for boundary value problem of p-Laplacian fractional differential equation with a sign-changed nonlinearity

Abstract

This paper investigates the existence of a unique positive solution for a class of boundary value problems of p-Laplacian fractional differential equations, where its nonlinearity is signchanged and involves a fractional derivative term, and its boundary involves a nonlinear fractional integral term. By constructing an appropriate auxiliary boundary value problem and applying a generalized fixed point theorem of sum operator and properties of Mittag-Leffler function, some sufficient conditions for the existence of a unique positive solution are presented, and a monotone iterative sequence uniformly converging to the unique solution is constructed. In addition, an example is given to illustrate the main result.

Keywords

• fractional boundary value problem
• p-Laplacian operator
• positive solution
• fixed point theorem of sum operator
• Mittag-Leffler function