Analysis and numerical approximation of the fractional-order two-dimensional diffusion-wave equation - Rafaqat, Kanza; Naeem, Muhammad; Akgül, Ali; Hassan, Ahmed M.; Abdullah, Farah Aini; Ali, Umair (Frontiers in Physics, 2023)
Non-local fractional derivatives are generally more effective in mimicking real-world phenomena and offer more precise representations of physical entities, such as the oscillation of earthquakes and the behavior of polymers. This study aims to solve the 2D fractional order diffusion-wave equation (FO-DWE) using the Riemann-Liouville (RL) time-fractional derivative. The FO-DWE is solved using the modified implicit approach based on the RL integral sense. The theoretical analysis is investigated for the suggested scheme such as stability, consistency, and convergence by using Fourier series analysis. The scheme is shown to be unconditionally stable, and the approximate solution is consistent and convergent to the exact result. A numerical example is given to demonstrate that the technique is more workable and feasible.