# Cantor Waves for Signorini Hyperelastic Materials with Cylindrical Symmetry

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## Abstract

**:**

## 1. Introduction

## 2. Cantor Metric Tensor

## 3. Local Fractional Calculus

#### 3.1. Yang Local Fractional Derivative

#### 3.2. Local Fractional Covariant Derivatives in Cantor Cylindrical Coordinates

## 4. Local Fractional Covariant Equations in Cylindrical Coordinates for Signorini Hyperelastic Materials

#### 4.1. Signorini Hyperelastic Materials

#### 4.2. Fractional Covariant Equations

#### 4.3. Fractional Differential Equations for Longitudinal Waves

## 5. Local Fractional Longitudinal Waves on Cantor Coordinates

^{th}power, and for the physical parameters $\lambda ,\mu ,c$ the dependence on the local fractional derivatives is expressed by the presence of the Gamma function. In order to analyze the fractal shape of solution, we consider the linear approximation.

#### Linear Equation

## 6. Conclusions

## Funding

## Conflicts of Interest

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**Figure 1.**The local fractional solution of Equation (17) for the longitudinal displacement on Cantor coordinates ($\alpha =0.7)$ compared with the smooth solution ($\alpha =1)$.

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**MDPI and ACS Style**

Cattani, C. Cantor Waves for Signorini Hyperelastic Materials with Cylindrical Symmetry. *Axioms* **2020**, *9*, 22.
https://doi.org/10.3390/axioms9010022

**AMA Style**

Cattani C. Cantor Waves for Signorini Hyperelastic Materials with Cylindrical Symmetry. *Axioms*. 2020; 9(1):22.
https://doi.org/10.3390/axioms9010022

**Chicago/Turabian Style**

Cattani, Carlo. 2020. "Cantor Waves for Signorini Hyperelastic Materials with Cylindrical Symmetry" *Axioms* 9, no. 1: 22.
https://doi.org/10.3390/axioms9010022