# Oscillators Based on Fractional-Order Memory Elements

## Abstract

**:**

## 1. Introduction

## 2. Preliminaries

#### 2.1. Definition of Fractional-Order Operator

#### 2.2. Numerical Solution of Fractional Differential Equation

## 3. Fractional-Order Memristive Elements

#### 3.1. Memristor

#### 3.2. Memcapacitor

#### 3.3. Meminductor

## 4. Models of the Fractional-Order Chaotic Systems

#### 4.1. Memcapacitor–Meminductor Oscillator

#### 4.2. Memristor–Memcapacitor–Meminductor Oscillator

## 5. Discussion

## 6. Conclusions

## Funding

## Institutional Review Board Statement

## Informed Consent Statement

## Data Availability Statement

## Conflicts of Interest

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**Figure 2.**Chaotic oscillator circuit based on two memory elements [31].

**Figure 5.**Orbits of the fractional-order oscillator (22) in state spaces $x-y-z$, $u-w-v$, respectively.

**Figure 6.**One-scroll attractors of the system (22) in state space $x-y-z$ (

**left**) and $u-w-v$ (

**right**).

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**MDPI and ACS Style**

Petráš, I.
Oscillators Based on Fractional-Order Memory Elements. *Fractal Fract.* **2022**, *6*, 283.
https://doi.org/10.3390/fractalfract6060283

**AMA Style**

Petráš I.
Oscillators Based on Fractional-Order Memory Elements. *Fractal and Fractional*. 2022; 6(6):283.
https://doi.org/10.3390/fractalfract6060283

**Chicago/Turabian Style**

Petráš, Ivo.
2022. "Oscillators Based on Fractional-Order Memory Elements" *Fractal and Fractional* 6, no. 6: 283.
https://doi.org/10.3390/fractalfract6060283