Akademik Veri Yönetim Sistemi
PRAMANA-JOURNAL OF PHYSICS, cilt.99, sa.4, 2025 (SCI-Expanded, Scopus)
This research extensively investigates the solitary wave solutions of the time-fractional Murray equation (TFME), a prevalent framework in diverse scientific and engineering disciplines. Three mathematical methods, the extended simple equation method, the modified extended auxiliary equation mapping method and the modified F-expansion method, are employed to derive analytical solutions in the form of trigonometric, hyperbolic, exponential and rational functions. To analyse the physical behaviour of the concerned model, some solutions are plotted in two and three dimensions by imparting particular values to the parameters under the constraint condition of each selective solution. Mathematica 13.0, the computational software, is used to handle all calculations as well as all plotted graphs of the concerned solutions. The derived results have numerous applications to understand the fluid dynamics and wave propagation, particularly in biological systems and potentially in modelling tsunami waves. Hence, this study has applications in nonlinear science. It is vital to perceive that our proposed methods are genuine, suitable and well-ordered for nonlinear fractional partial differential equations (NLFPDEs).