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 …
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 …
problems due to its high-order accuracy, while the corresponding numerical analysis is …
Forward and backward problems for coupled subdiffusion systems
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 …
time-fractional diffusion equations, encompassing scenarios of strong coupling. For the …
Numerical energy dissipation for time-fractional phase-field equations
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 …
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
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 …
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
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 …
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
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 …
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 …
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
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 …
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
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 …
constructed for the time fractional Cahn–Hilliard model. Nonuniform L1+ formula is utilized …