169 citations
Counting papers with at most 25 authors, so collaboration author lists do not stand in for the people here.
- University of StuttgartDE7 papers
- Max Planck Institute for Intelligent SystemsDE6 papers
- Darmstadt University of Applied SciencesDE5 papers
- Institute of MathematicsPL4 papers
- Vietnam Academy of Science and TechnologyVN4 papers
- European UnionBE3 papers
- Centre National de la Recherche ScientifiqueFR2 papers
- Friedrich-Alexander-Universität Erlangen-NürnbergDE2 papers
- Institute of PhysicsPL2 papers
- Kavli Institute for Theoretical SciencesCN2 papers
- National Research University Higher School of EconomicsRU2 papers
- Radboud University NijmegenNL2 papers
10 papers · 1 filter
Revisiting Diffusive Representations for Enhanced Numerical Approximation of Fractional Integrals
Renu Chaudhary, Kai Diethelm
This study reexamines diffusive representations for fractional integrals with the goal of pioneering new variants of such representations. These variants aim to offer highly effici…
Novel Variants of Diffusive Representation of Fractional Integrals: Construction and Numerical Computation
Renu Chaudhary, Kai Diethelm
In this paper, we revisit the diffusive representations of fractional integrals established in \cite{diethelm2023diffusive} to explore novel variants of such representations which…
A constructive approach for investigating the stability of incommensurate fractional differential systems
Kai Diethelm, Safoura Hashemishahraki, Ha Duc Thai +1
This paper is devoted to studying the asymptotic behaviour of solutions to generalized non-commensurate fractional systems. To this end, we first consider fractional systems with r…
Reconstruction Formulae for 3D Field-Free Line Magnetic Particle Imaging
Vladyslav Gapyak, Thomas März, Andreas Weinmann
Magnetic Particle Imaging (MPI) is a promising noninvasive in vivo imaging modality that makes it possible to map the spatial distribution of superparamagnetic nanoparticles by exp…
A new approach to shooting methods for terminal value problems of fractional differential equations
Kai Diethelm, Frank Uhlig
For terminal value problems of fractional differential equations of order that use Caputo derivatives, shooting methods are a well developed and investigated approach.…
Diffusive Representations for the Numerical Evaluation of Fractional Integrals
Kai Diethelm
Diffusive representations of fractional differential and integral operators can provide a convenient means to construct efficient numerical algorithms for their approximate evaluat…
Smoothing splines for discontinuous signals
Martin Storath, Andreas Weinmann
Smoothing splines are twice differentiable by construction, so they cannot capture potential discontinuities in the underlying signal. In this work, we consider a special case of t…
A New Diffusive Representation for Fractional Derivatives, Part II: Convergence Analysis of the Numerical Scheme
Kai Diethelm
Recently, we have proposed a new diffusive representation for fractional derivatives and, based on this representation, suggested an algorithm for their numerical computation. From…
Fast Solution Methods for Fractional Differential Equations in the Modeling of Viscoelastic Materials
Kai Diethelm
Fractional order models have proven to be a very useful tool for the modeling of the mechanical behaviour of viscoelastic materials. Traditional numerical solution methods exhibit…
Smoothing for signals with discontinuities using higher order Mumford-Shah models
Martin Storath, Lukas Kiefer, Andreas Weinmann
Minimizing the Mumford-Shah functional is frequently used for smoothing signals or time series with discontinuities. A significant limitation of the standard Mumford-Shah model is…