155 citations · 487 across the 17 of their papers we have counts for
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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…
A New Diffusive Representation for Fractional Derivatives and its Application
Kai Diethelm
Diffusive representations of fractional derivatives have proven to be useful tools in the construction of fast and memory efficient numerical methods for solving fractional differe…
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…
Error Bounds for the Numerical Integration of Functions with Limited Smoothness
Kai Diethelm
Recently, Trefethen (SIAM Review 50 (2008), 67--87) and Xiang and Bornemann (SIAM J. Numer. Anal. 50 (2012), 2581--2587) investigated error bounds for n-point Gauss and Clenshaw-Cu…