Abstract:
In this article, the two-dimensional time fractional unsteady convection diffusion system is under consideration. In particular, these practicable implications include turbulence, heat transfer, fluid flow, traffic flow, and modeling of gas dynamics. The existence of results and uniqueness is proved by applying the fixed-point theory with the help of some well-known results and theorems such as the contraction mapping theorem with Lipschitz condition, and Schauder's fixed point theorem. Mainly, we find the exact solitary wave solutions of the underlying model. For this sake, the new extended direct algebraic method is applied and the solutions are obtained in the form of dark, singular, complex, combo, trigonometric and rational solutions. Further, wedraw 3D plots to show the behavior of these solutions by choosing the differentvalues of parameters. The aim of this study is to investigate the advantage of using the mixed physics informed neural networks (MPINN) to perform asimulation for such phenomena. A hypothetical situation was considered in which an obstacle arose at the channel of the ureter during its peristaltic motion.This situation is known as a kidney stone disease. The momentum conservation governing equations is considered for the case of incompressible Newtonian fluidand the dimensionless corresponding form is introduced. The contour plots of thepressure and the velocity fields are illustrated for different stone shapes. Also,the shear stress is obtained at the surface of Lumen. Our findings show the applicability of the MPINN for obtaining reliable results for such crucial situations.
Page(s):
157-157
DOI:
DOI not available
Published:
Journal: 4th International Conference of Sciences “Revamped Scientific Outlook of 21st Century, 2025” , November 12,2025, Volume: 1, Issue: 1, Year: 2025
Keywords:
Caputo operator
,
Existence
,
Compactness
,
New extended direct algebraic method
,
Solitons solutions
,
Wave transformation