3 citations · 6 across the 8 of their papers we have counts for
8 papers
Error of discretization of Caputo fractional derivative in weighted spaces
Łukasz Płociniczak, Hubert Woszczek
We establish uniform error bounds of the L1 discretization of the Caputo fractional derivative of the function from the weighted Sobolev space with weight belonging to the Mucknenh…
Self-similar solutions to the time-fractional Porous-Medium Equation
David Gómez-Castro, Łukasz Płociniczak, Juan Luis Vázquez
We show the existence of self-similar solutions with constant finite mass to the time-fractional Porous-Medium Equation for all spatial dimensions and all exponents $m>m_…
Asymmetric Lévy walks driven by convex combination of fractional material derivatives
Łukasz Płociniczak, Marek A. Teuerle, Hubert Woszczek
We analyze a class of linear partial differential equations that arise as deterministic descriptions of the scaling limits of Lévy walks, in which transport is driven by a convex c…
A note on the L1 discretization error for the Caputo derivative in Hölder spaces
Félix del Teso, Łukasz Płociniczak
We establish uniform error bounds of the L1 discretization of the Caputo derivative of Hölder continuous functions. The result can be understood as: error = (degree of smoothness -…
Fractional material derivative: pointwise representation and a finite volume numerical scheme
Łukasz Płociniczak, Marek A. Teuerle
The fractional material derivative appears as the fractional operator that governs the dynamics of the scaling limits of Lévy walks - a stochastic process that originates from the…
Numerical methods and regularity properties for viscosity solutions of nonlocal in space and time diffusion equations
Félix del Teso, Łukasz Płociniczak
We consider a general family of nonlocal in space and time diffusion equations with space-time dependent diffusivity and prove convergence of finite difference schemes in the conte…
Convolution Quadrature for the quasilinear subdiffusion equation
Maria López-Fernández, Łukasz Płociniczak
We construct a Convolution Quadrature (CQ) scheme for the quasilinear subdiffusion equation of order and supply it with the fast and oblivious implementation. In particular, we…
Fully discrete Galerkin scheme for a semilinear subdiffusion equation with nonsmooth data and time-dependent coefficient
Łukasz Płociniczak, Kacper Taźbierski
We couple the L1 discretization of the Caputo fractional derivative in time with the Galerkin scheme to devise a linear numerical method for the semilinear subdiffusion equation. T…