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
Abstract
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.