# Adaptive Fuzzy Control for Nonlinear Fractional-Order Uncertain Systems with Unknown Uncertainties and External Disturbance

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## Abstract

**:**

## 1. Introduction

## 2. Problem formulation and preliminaries

**Definition 1**(Caputo Fractional Derivative).

**Definition 2**(Mittag–Leffler Function).

**Lemma 1**

**Lemma 2.**

**Proof.**

## 3. Description of the Fuzzy Logic System

## 4. Adaptive Fuzzy Controller Design

**Theorem 1.**

**Proof.**

## 5. Numerical Simulations

## 6. Conclusions

## Acknowledgments

## Author Contributions

## Conflicts of Interest

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**MDPI and ACS Style**

Li, L.; Sun, Y.
Adaptive Fuzzy Control for Nonlinear Fractional-Order Uncertain Systems with Unknown Uncertainties and External Disturbance. *Entropy* **2015**, *17*, 5580-5592.
https://doi.org/10.3390/e17085580

**AMA Style**

Li L, Sun Y.
Adaptive Fuzzy Control for Nonlinear Fractional-Order Uncertain Systems with Unknown Uncertainties and External Disturbance. *Entropy*. 2015; 17(8):5580-5592.
https://doi.org/10.3390/e17085580

**Chicago/Turabian Style**

Li, Ling, and Yeguo Sun.
2015. "Adaptive Fuzzy Control for Nonlinear Fractional-Order Uncertain Systems with Unknown Uncertainties and External Disturbance" *Entropy* 17, no. 8: 5580-5592.
https://doi.org/10.3390/e17085580