5 papers
Error of discretization of Caputo fractional derivative in weighted spaces
Åukasz PÅociniczak, 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, Åukasz PÅociniczak, 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
Åukasz PÅociniczak, 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…
Convolution Quadrature for the quasilinear subdiffusion equation
Maria López-Fernández, Åukasz PÅociniczak
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, w…
A note on the L1 discretization error for the Caputo derivative in Hölder spaces
Félix del Teso, Åukasz PÅociniczak
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…