# Exact Solutions to Time-Fractional Fifth Order KdV Equation by Trial Equation Method Based on Symmetry

## Abstract

**:**

## 1. Introduction

- (i)
- ${D}_{t}^{\alpha}(f(g(t))={t}^{1-\alpha}{g}^{\alpha -1}{g}^{\prime}(t){D}_{g}^{\alpha}f(g)={t}^{1-\alpha}{g}^{\prime}(t){f}^{\prime}(g)$;
- (ii)
- ${D}_{t}^{\alpha}f(t)={t}^{1-\alpha}{f}^{\prime}(t)$.

## 2. Outline of trial Equation Method

**Remark**. For some differential equations, in the trial Equation (5), $F(u)$ is perhaps a more general functions rather than a polynomial. There exist no general principle to give the form of trial equation, so we need a trial procedure to choose it according to the structure of the considered problem. We can find more details of the trial equation method in a series of Liu’s papers [29,30,31,32,33].

## 3. Exact Solutions of FKdV Equation

## 4. Conclusions and Discussions

## Author Contributions

## Funding

## Conflicts of Interest

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**MDPI and ACS Style**

Liu, T.
Exact Solutions to Time-Fractional Fifth Order KdV Equation by Trial Equation Method Based on Symmetry. *Symmetry* **2019**, *11*, 742.
https://doi.org/10.3390/sym11060742

**AMA Style**

Liu T.
Exact Solutions to Time-Fractional Fifth Order KdV Equation by Trial Equation Method Based on Symmetry. *Symmetry*. 2019; 11(6):742.
https://doi.org/10.3390/sym11060742

**Chicago/Turabian Style**

Liu, Tao.
2019. "Exact Solutions to Time-Fractional Fifth Order KdV Equation by Trial Equation Method Based on Symmetry" *Symmetry* 11, no. 6: 742.
https://doi.org/10.3390/sym11060742