Acoustic wave structures for the confirmable time-fractional Westervelt equation in ultrasound imaging

Tahira Sumbal Shaikh; Muhammad Zafarullah Baber; Nauman Ahmed; Muhammad Sajid Iqbal; Ali Akgül; Sayed M. El Din

Results in Physics (Jun 2023)

Acoustic wave structures for the confirmable time-fractional Westervelt equation in ultrasound imaging

Tahira Sumbal Shaikh,
Muhammad Zafarullah Baber,
Nauman Ahmed,
Muhammad Sajid Iqbal,
Ali Akgül,
Sayed M. El Din

Affiliations

Tahira Sumbal Shaikh: Department of Mathematics, Lahore College for Women University, Lahore, Pakistan
Muhammad Zafarullah Baber: Department of Mathematics and Statistics, The University of Lahore, Lahore, Pakistan
Nauman Ahmed: Department of Mathematics and Statistics, The University of Lahore, Lahore, Pakistan; Department of Computer Science and Mathematics, Lebanese American University, Beirut, Lebanon; Corresponding author.
Muhammad Sajid Iqbal: Department of Humanities & Basic Science, Military College of Signals, National University of Science and Technology, Islamabad, Pakistan
Ali Akgül: Department of Computer Science and Mathematics, Lebanese American University, Beirut, Lebanon; Siirt University, Art and Science Faculty, Department of Mathematics, TR 56100, Siirt Turkey; Near East University, Mathematics Research Center, Department of Mathematics, Near East Boulevard, PC: 99138, Nicosia/Mersin 10, Turkey; Corresponding author at: Siirt University, Art and Science Faculty, Department of Mathematics, TR 56100, Siirt Turkey.
Sayed M. El Din: Center of Research, Faculty of Engineering, Future University in Egypt, New Cairo 11835, Egypt

Journal volume & issue: Vol. 49
p. 106494

Abstract

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In this study, the acoustic nonlinear equation namely the confirmable time-fractional Westervelt equation is under consideration analytically. This equation is applicable in the wave propagation of sound and high amplitude in medical imaging and therapy. The different types of wave structures are constructed for the confirmable time-fractional Westervelt equation by using two different techniques namely as, the modified exponential rational functional method and the modified G′/G2-model expansion method. With the help of these two techniques, we gain the different hyperbolic, exponential, periodic, and plane wave function solutions. Additionally, to show the graphical behavior of the wave structure, the 3D, 2D, and their corresponding contour representations are drawn by the different choices of parameters.

Published in Results in Physics

ISSN: 2211-3797 (Online)
Publisher: Elsevier
Country of publisher: Netherlands
LCC subjects: Science: Physics
Website: http://www.journals.elsevier.com/results-in-physics/

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