# Transient Propagation of Spherical Waves in Porous Material: Application of Fractional Calculus

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## Abstract

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## 1. Introduction

## 2. Fractional Model for Porous Media

## 3. Solution of the Fractional Spherical-Wave Equation

## 4. Green Function of the Porous Medium in the Time Domain

## 5. Analytical Solution in the Time Domain

## 6. Discussion and Conclusions

## Author Contributions

## Funding

## Institutional Review Board Statement

## Informed Consent Statement

## Data Availability Statement

## Conflicts of Interest

## Appendix A. Calculus of $\mathit{D}\left(\mathit{t}\right)={\mathcal{L}}^{-1}\left(\right)open="["\; close="]">\frac{1}{\mathit{k}\left(\mathit{s}\right)}$

## Appendix B. Calculus of $\mathit{S}\left(\mathit{t}\right)={\mathcal{L}}^{-1}\left(\right)open="("\; close=")">\frac{1}{{\mathit{k}}^{2}\left(\mathit{s}\right)}$

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**MDPI and ACS Style**

Fellah, Z.E.A.; Fellah, M.; Roncen, R.; Ongwen, N.O.; Ogam, E.; Depollier, C.
Transient Propagation of Spherical Waves in Porous Material: Application of Fractional Calculus. *Symmetry* **2022**, *14*, 233.
https://doi.org/10.3390/sym14020233

**AMA Style**

Fellah ZEA, Fellah M, Roncen R, Ongwen NO, Ogam E, Depollier C.
Transient Propagation of Spherical Waves in Porous Material: Application of Fractional Calculus. *Symmetry*. 2022; 14(2):233.
https://doi.org/10.3390/sym14020233

**Chicago/Turabian Style**

Fellah, Zine El Abiddine, Mohamed Fellah, Rémi Roncen, Nicholas O. Ongwen, Erick Ogam, and Claude Depollier.
2022. "Transient Propagation of Spherical Waves in Porous Material: Application of Fractional Calculus" *Symmetry* 14, no. 2: 233.
https://doi.org/10.3390/sym14020233