Fractional wave models and their experimental applications

BA Malomed - Fractional Dispersive Models and Applications: Recent …, 2024 - Springer
A focused summary of one-and two-dimensional models for linear and nonlinear wave
propagation in fractional media is given. The basic models, which represent fractional …

Numerical analysis for optimal quadratic spline collocation method in two space dimensions with application to nonlinear time-fractional diffusion equation

X Ye, X Zheng, J Liu, Y Liu - Advances in Computational Mathematics, 2024 - Springer
Optimal quadratic spline collocation (QSC) method has been widely used in various
problems due to its high-order accuracy, while the corresponding numerical analysis is …

Forward and backward problems for coupled subdiffusion systems

D Feng, Y Liu, S Lu - Numerical Functional Analysis and …, 2025 - Taylor & Francis
In this article, we investigate both forward and backward problems for coupled systems of
time-fractional diffusion equations, encompassing scenarios of strong coupling. For the …

Numerical energy dissipation for time-fractional phase-field equations

C Quan, T Tang, J Yang - arxiv preprint arxiv:2009.06178, 2020 - arxiv.org
The numerical integration of phase-field equations is a delicate task which needs to recover
at the discrete level intrinsic properties of the solution such as energy dissipation and …

Recovery of multiple parameters in subdiffusion from one lateral boundary measurement

S Cen, B **, Y Liu, Z Zhou - Inverse Problems, 2023 - iopscience.iop.org
This work is concerned with numerically recovering multiple parameters simultaneously in
the subdiffusion model from one single lateral measurement on a part of the boundary, while …

Estimates for coefficients in Jacobi series for functions with limited regularity by fractional calculus

G Liu, W Liu, B Duan - Advances in Computational Mathematics, 2024 - Springer
In this paper, optimal estimates on the decaying rates of Jacobi expansion coefficients are
obtained by fractional calculus for functions with algebraic and logarithmic singularities. This …

Weak maximum principle of finite element methods for parabolic equations in polygonal domains

G Bai, D Leykekhman, B Li - Numerische Mathematik, 2025 - Springer
The weak maximum principle of finite element methods for parabolic equations is proved for
both semi-discretization in space and fully discrete methods with k-step backward …

Long time decay analysis of complex-valued fractional abstract evolution equations with delay

Z Yao, Z Yang, Y Fu - Applied Mathematics and Computation, 2024 - Elsevier
The asymptotic stability and long time decay rates of solutions to linear Caputo time-
fractional ordinary differential equations are known to be completely determined by the …

Correction of a High-Order Numerical Method for Approximating Time-Fractional Wave Equation

M Ramezani, R Mokhtari, Y Yan - Journal of Scientific Computing, 2024 - Springer
A high-order time discretization scheme to approximate the time-fractional wave equation
with the Caputo fractional derivative of order α∈(1, 2) is studied. We establish a high-order …

Variable-step numerical schemes and energy dissipation laws for time fractional Cahn–Hilliard model

R Qi, W Zhang, X Zhao - Applied Mathematics Letters, 2024 - Elsevier
Two temporal second-order energy stable schemes with variable time step sizes are
constructed for the time fractional Cahn–Hilliard model. Nonuniform L1+ formula is utilized …