An error estimate of a numerical approximation to a hidden-memory variable-order space-time fractional diffusion equation
Variable-order space-time fractional diffusion equations, in which the variation of the
fractional orders determined by the fractal dimension of the media via the Hurst index …
fractional orders determined by the fractal dimension of the media via the Hurst index …
Optimal-order error estimates of finite element approximations to variable-order time-fractional diffusion equations without regularity assumptions of the true solutions
We study a fully discretized finite element approximation to variable-order Caputo and
Riemann–Liouville time-fractional diffusion equations (tFDEs) in multiple space dimensions …
Riemann–Liouville time-fractional diffusion equations (tFDEs) in multiple space dimensions …
Analysis of a dilute polymer model with a time-fractional derivative
We investigate the well-posedness of a coupled Navier–Stokes–Fokker–Planck system with
a time-fractional derivative. Such systems arise in the kinetic theory of dilute solutions of …
a time-fractional derivative. Such systems arise in the kinetic theory of dilute solutions of …
Convergence guarantees for coefficient reconstruction in PDEs from boundary measurements by variational and Newton-type methods via range invariance
B Kaltenbacher - IMA Journal of Numerical Analysis, 2024 - academic.oup.com
A key observation underlying this paper is the fact that the range invariance condition for
convergence of regularization methods for nonlinear ill-posed operator equations—such as …
convergence of regularization methods for nonlinear ill-posed operator equations—such as …
Fractionalization of anti-Zener and Zener models via rheological analogy
S Jelić, D Zorica - Acta Mechanica, 2023 - Springer
Fractional-order anti-Zener and Zener models are formulated using rheological schemes
corresponding to the classical anti-Zener and Zener models and by considering fractional …
corresponding to the classical anti-Zener and Zener models and by considering fractional …
Energy balance for fractional anti-Zener and Zener models in terms of relaxation modulus and creep compliance
S Jelić, D Zorica - Applied Mathematical Modelling, 2023 - Elsevier
Considering the linear constitutive model containing fractional integrals and Riemann-
Liouville fractional derivatives, the power per unit volume is expressed in time domain in …
Liouville fractional derivatives, the power per unit volume is expressed in time domain in …
A posteriori error analysis for approximations of time-fractional subdiffusion problems
L Banjai, C Makridakis - Mathematics of Computation, 2022 - ams.org
In this paper we consider a sub-diffusion problem where the fractional time derivative is
approximated either by the L1 scheme or by Convolution Quadrature. We propose new …
approximated either by the L1 scheme or by Convolution Quadrature. We propose new …
On an inverse problem of nonlinear imaging with fractional damping
B Kaltenbacher, W Rundell - Mathematics of Computation, 2022 - ams.org
This paper considers the attenuated Westervelt equation in pressure formulation. The
attenuation is by various models proposed in the literature and characterised by the …
attenuation is by various models proposed in the literature and characterised by the …
[HTML][HTML] The vanishing relaxation time behavior of multi-term nonlocal Jordan–Moore–Gibson–Thompson equations
B Kaltenbacher, V Nikolić - Nonlinear Analysis: Real World Applications, 2024 - Elsevier
Abstract The family of Jordan–Moore–Gibson–Thompson (JMGT) equations arises in
nonlinear acoustics when a relaxed version of the heat flux law is employed within the …
nonlinear acoustics when a relaxed version of the heat flux law is employed within the …
Limiting behavior of quasilinear wave equations with fractional-type dissipation
In this work, we investigate a class of quasilinear wave equations of Westervelt type with, in
general, nonlocal-in-time dissipation. They arise as models of nonlinear sound propagation …
general, nonlocal-in-time dissipation. They arise as models of nonlinear sound propagation …