# Symmetry Group Classification and Conservation Laws of the Nonlinear Fractional Diffusion Equation with the Riesz Potential

^{*}

^{†}

## Abstract

**:**

## 1. Introduction

## 2. Preliminaries

**Remark**

**1.**

**Theorem**

**1**

**Theorem**

**2.**

**Proposition**

**1**

**Theorem**

**3.**

**Corollary**

**1.**

## 3. Group Classification of the Nonlinear Space-Fractional Porous Medium Equation

- $k\left(u\right)$ is an arbitrary function;
- $k\left(u\right)={e}^{u}$;
- $k\left(u\right)={(u+A)}^{\sigma}$, $\sigma \ne 0$, $A=const$;
- $k\left(u\right)=1$.

**Theorem**

**4.**

## 4. Nonlinear Self-Adjointness

**Proof.**

## 5. Conservation Laws

## Author Contributions

## Funding

## Conflicts of Interest

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**MDPI and ACS Style**

Belevtsov, N.S.; Lukashchuk, S.Y.
Symmetry Group Classification and Conservation Laws of the Nonlinear Fractional Diffusion Equation with the Riesz Potential. *Symmetry* **2020**, *12*, 178.
https://doi.org/10.3390/sym12010178

**AMA Style**

Belevtsov NS, Lukashchuk SY.
Symmetry Group Classification and Conservation Laws of the Nonlinear Fractional Diffusion Equation with the Riesz Potential. *Symmetry*. 2020; 12(1):178.
https://doi.org/10.3390/sym12010178

**Chicago/Turabian Style**

Belevtsov, Nikita S., and Stanislav Yu. Lukashchuk.
2020. "Symmetry Group Classification and Conservation Laws of the Nonlinear Fractional Diffusion Equation with the Riesz Potential" *Symmetry* 12, no. 1: 178.
https://doi.org/10.3390/sym12010178