New Soliton Solutions of M-fractional Westervelt Model in Ultrasound Imaging via Two Analytical Techniques

Haitham Qawaqneh; Asim Zafar; Muhammad Raheel; Abdullah A. Zaagan; Emad H.M. Zahran; Adem Cevikel; Ahmet Bekir

doi:10.20944/preprints202309.2163.v1

A peer-reviewed article of this Preprint also exists.

Qawaqneh, H.; Zafar, A.; Raheel, M.; Zaagan, A.A.; Zahran, E.H.M.; Cevikel, A.; Bekir, A. New Soliton Solutions of M-Fractional Westervelt Model in Ultrasound Imaging via Two Analytical Techniques. Optical and Quantum Electronics 2024, 56, doi:10.1007/s11082-024-06371-1. Qawaqneh, H.; Zafar, A.; Raheel, M.; Zaagan, A.A.; Zahran, E.H.M.; Cevikel, A.; Bekir, A. New Soliton Solutions of M-Fractional Westervelt Model in Ultrasound Imaging via Two Analytical Techniques. Optical and Quantum Electronics 2024, 56, doi:10.1007/s11082-024-06371-1.

Abstract

This research paper is about to obtain 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. At the end, these techniques are simple, fruitful and effective to deal with nonlinear FPDEs.

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Copyright: This is an open access article distributed under the Creative Commons Attribution License which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.

New Soliton Solutions of M-fractional Westervelt Model in Ultrasound Imaging via Two Analytical Techniques

Abstract

Keywords

Subject

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