Existence and uniqueness of positive solutions of boundary-value problems for fractional differential equations with p-Laplacian operator

TL;DR

This paper investigates the existence, nonexistence, and uniqueness of positive solutions for boundary-value problems involving nonlinear fractional differential equations with p-Laplacian operators, using Green functions and fixed point theorems.

Contribution

It provides new conditions for existence, nonexistence, and uniqueness of positive solutions in fractional p-Laplacian boundary-value problems.

Findings

Established existence of positive solutions under certain parameter conditions.

Identified parameter ranges where positive solutions do not exist.

Proved uniqueness of positive solutions within specific parameter sets.

Abstract

In this article, we consider the boundary-value problem of nonlinear fractional differential equation with p-Laplacian operator. By the properties of Green function and Schauder fixed point theorem, several existence and nonexistence results for positive solutions, in terms of two parameters are obtained. The uniqueness of positive solution on these parameters is also studied.