# Positive solutions of $p$-Laplacian fractional differential equations with fractional derivative boundary condition

## TL;DR

This paper investigates the existence and uniqueness of positive solutions for p-Laplacian fractional differential equations with fractional boundary conditions, using fixed point theorems and providing illustrative examples.

## Contribution

It introduces new conditions for positive solutions of p-Laplacian fractional equations with fractional boundary conditions, employing Krasnosel'skii's theorem and related methods.

## Key findings

- Existence of positive solutions established under certain conditions
- Uniqueness of solutions proved using contraction mapping
- Examples demonstrate the applicability of the theoretical results

## Abstract

In this paper, we show some results about the existence and the uniqueness of the positive solution for a $p$-Laplacian fractional differential equations with fractional derivative boundary condition. Our results are based on Krasnosel'skii's fixed point theorem, the nonlinear alternative of Leray-Schauder type and contraction mapping principle. Three examples are given to illustrate the applicability of our main results.