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 …

We study a fully discretized finite element approximation to variable-order Caputo and
Riemann–Liouville time-fractional diffusion equations (tFDEs) in multiple space dimensions …

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 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 …

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 …

Considering the linear constitutive model containing fractional integrals and Riemann-
Liouville fractional derivatives, the power per unit volume is expressed in time domain in …

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 …

This paper considers the attenuated Westervelt equation in pressure formulation. The
attenuation is by various models proposed in the literature and characterised by the …

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 …

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 …