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

Frontiers in Physics

Physics

Muhammad Naeem¹  Kanza Rafaqat²  Umair Ali²  Ali Akgül³  Ahmed M. Hassan⁴  Farah Aini Abdullah⁵ 

[1] College of Mathematical Sciences, Umm Al-Qura University, Makkah, Saudi Arabia;Department of Applied Mathematics and Statistics, Institute of Space Technology, Islamabad, Pakistan;Department of Computer Science and Mathematics, Lebanese American University, Beirut, Lebanon;Department of Mathematics, Art and Science Faculty, Siirt University, Siirt, Türkiye;Mathematics Research Center, Department of Mathematics, Near East University, Nicosia, Türkiye;Faculty of Engineering, Future University in Egypt, New Cairo, Egypt;School of Mathematical Sciences, Universiti Sains Malaysia, Gelugor, Penang, Malaysia;

关键词: fractional-order diffusion-wave equation;    implicit scheme;    Riemann–Liouville fractional integral operator;    stability;    consistency;    convergence;   

DOI  :  10.3389/fphy.2023.1199665

 received in 2023-04-03, accepted in 2023-08-21,  发布年份 2023

来源: Frontiers

【 摘 要 】

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.

【 授权许可】

Unknown   
Copyright © 2023 Rafaqat, Naeem, Akgül, Hassan, Abdullah and Ali.