AUTHOR=Rafaqat Kanza , Naeem Muhammad , Akgül Ali , Hassan Ahmed M. , Abdullah Farah Aini , Ali Umair 

TITLE=Analysis and numerical approximation of the fractional-order two-dimensional diffusion-wave equation

JOURNAL=Frontiers in Physics

VOLUME=11

YEAR=2023

URL=https://www.frontiersin.org/journals/physics/articles/10.3389/fphy.2023.1199665

DOI=10.3389/fphy.2023.1199665

ISSN=2296-424X

ABSTRACT=<p>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 using the Riemann–Liouville time-fractional derivative. The fractional-order diffusion-wave equation is solved using the modified implicit approach based on the Riemann–Liouville 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 provided to demonstrate that the technique is more workable and feasible.</p>