# A Multi-Stage Homotopy Perturbation Method for the Fractional Lotka-Volterra Model

^{*}

## Abstract

**:**

## 1. Introduction

## 2. Preliminaries

**Definition**

**1.**

**Definition**

**2.**

**Lemma**

**1.**

**Proof.**

**Lemma**

**2.**

**Proof.**

## 3. Main Result

**Theorem**

**1.**

**Proof.**

#### Convergence

## 4. Examples

**Case**

**1.**

**Case**

**2.**

## 5. Conclusions

## Author Contributions

## Funding

## Conflicts of Interest

## Abbreviations

HPM | Homotopy perturbation method |

MHPM | Multistage homotopy perturbation method |

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**MDPI and ACS Style**

Arciga-Alejandre, M.P.; Sanchez-Ortiz, J.; Ariza-Hernandez, F.J.; Catalan-Angeles, G.
A Multi-Stage Homotopy Perturbation Method for the Fractional Lotka-Volterra Model. *Symmetry* **2019**, *11*, 1330.
https://doi.org/10.3390/sym11111330

**AMA Style**

Arciga-Alejandre MP, Sanchez-Ortiz J, Ariza-Hernandez FJ, Catalan-Angeles G.
A Multi-Stage Homotopy Perturbation Method for the Fractional Lotka-Volterra Model. *Symmetry*. 2019; 11(11):1330.
https://doi.org/10.3390/sym11111330

**Chicago/Turabian Style**

Arciga-Alejandre, Martin P., Jorge Sanchez-Ortiz, Francisco J. Ariza-Hernandez, and Gabriel Catalan-Angeles.
2019. "A Multi-Stage Homotopy Perturbation Method for the Fractional Lotka-Volterra Model" *Symmetry* 11, no. 11: 1330.
https://doi.org/10.3390/sym11111330