New soliton solutions of M-fractional Westervelt model in ultrasound imaging via two analytical techniques

Abstract

This research paper is about the ultrasound propagation, which propagates the mechanical vibration of the molecules or of the particles of a material. It measures the speed of sound in air. Ultrasound imaging is being used in a well-established way to produce pictures of tissues inside the body of human beings. They are modeled in non-linear wave equations with high intensity. We obtained the new soliton solutions to the M-fractional ( 1+1)-dimensional nonlinear Westervelt model by utilizing exp(a) function and modified simplest equation techniques. The gained solutions involving dark, bright, periodic, dark-bright and other solitons. These results have many applications in wave propagation of sound waves, high amplitude in medical imaging and therapy. Achieved results are verified by Mathematica tool and the effect of M-fractional derivative on the solutions is explained through 2-Dimensional, 3-Dimensional and contour plots. The stability of the concerned model is also discussed. The images are prepared in a well-established way, showing the production of tissues inside the human body. At the end, these techniques are simple, fruitful and effective to deal with nonlinear FPDEs.