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FRACTIONAL CALCULUS OF THERMOELASTIC $p$ $p$ -WAVES REFLECTION UNDER INFLUENCE OF GRAVITY AND ELECTROMAGNETIC FIELDS

HAMMAD ALOTAIBI

Department of Mathematics, Faculty of Science, Taif University 888, Saudi Arabia

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S. M. ABO-DAHAB

Department of Mathematics, Faculty of Science, Taif University 888, Saudi Arabia

Department of Mathematics, Faculty of Science, South Valley University, Qena, Egypt

E-mail Address: sdahb@yahoo.com

Corresponding author.

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H. R. ABDLRAHIM

Sohag Industrial Technical Institute, Medium Valley Technological Collegue, Ministry of Higher Education, Egypt

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, and

A. A. KILANY

Department of Mathematics, Faculty of Science, Sohag University, Sohag, Egypt

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https://doi.org/10.1142/S0218348X2040037XCited by:15 (Source: Crossref)

This article is part of the issue:

Special Issue on Fractal and Fractional with Applications to Nature
Guest Editors: Abdon Atangana, Emile Franc Goufo Ndongmo, José Francisco Gómez Aguilar, Muhammad Altaf Khan and Ilknur Koca

Abstract

In this paper, we discussed the longitudinal harmonic waves reflection from a solid elastic half-space with electromagnetic and gravity fields influence, considering a fractional order via fractional exponential function method. The clarifications are required for the reflection amplitudes ratios (i.e. the ratios between the reflected waves amplitude and the incident waves amplitude). The results obtained were calculated analytically and displayed by graphs to show the physical meaning of the phenomenon. A comparison has been made between the fractional and integer derivatives. The results of this paper demonstrate the rigor and effectiveness of the considered fractional technique.

Keywords:

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Vol. 28, No. 08

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History

Received 11 January 2020

Accepted 6 March 2020

Published: June 18, 2020

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This is an Open Access article in the “Special Issue on Fractal and Fractional with Applications to Nature” published by World Scientific Publishing Company. It is distributed under the terms of the Creative Commons Attribution 4.0 (CC BY) License which permits use, distribution and reproduction in any medium, provided the original work is properly cited.

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FRACTIONAL CALCULUS OF THERMOELASTIC pp<math altimg="eq-00001.gif" display="inline"><mi>p</mi></math>-WAVES REFLECTION UNDER INFLUENCE OF GRAVITY AND ELECTROMAGNETIC FIELDS

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FRACTIONAL CALCULUS OF THERMOELASTIC $p$ $p$ -WAVES REFLECTION UNDER INFLUENCE OF GRAVITY AND ELECTROMAGNETIC FIELDS