37 Result(s)
within
Kai Diethelm
English
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Article
Open AccessA New Approach to Shooting Methods for Terminal Value Problems of Fractional Differential Equations
For terminal value problems of fractional differential equations of order \(\alpha \in (0,1)\) ...
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Chapter and Conference Paper
A New Diffusive Representation for Fractional Derivatives, Part I: Construction, Implementation and Numerical Examples
Diffusive representations of fractional derivatives have proven to be useful tools in the construction of fast and memory efficient numerical methods for solving fractional differential equations. A common cha...
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Article
Open AccessAsymptotic behaviour of solutions to non-commensurate fractional-order planar systems
This paper is devoted to studying non-commensurate fractional order planar systems. Our contributions are to derive sufficient conditions for the global attractivity of non-trivial solutions to fractional-orde...
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Article
Open AccessA Hilbert Space Approach to Fractional Differential Equations
We study fractional differential equations of Riemann–Liouville and Caputo type in Hilbert spaces. Using exponentially weighted spaces of functions defined on
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Article
Open AccessTrends, directions for further research, and some open problems of fractional calculus
The area of fractional calculus (FC) has been fast develo** and is presently being applied in all scientific fields. Therefore, it is of key relevance to assess the present state of development and to forese...
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Article
Open AccessUpper and lower estimates for the separation of solutions to fractional differential equations
Given a fractional differential equation of order \(\alpha \in (0,1]\) α ...
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Chapter and Conference Paper
Saving Energy Using the READEX Methodology
With today’s top supercomputers consuming several megawatts of power, optimization of energy consumption has become one of the major challenges on the road to exascale computing. The EU Horizon 2020 project RE...
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Article
Why Fractional Derivatives with Nonsingular Kernels Should Not Be Used
In recent years, many papers discuss the theory and applications of new fractional-order derivatives that are constructed by replacing the singular kernel of the Caputo or Riemann-Liouville derivative by a non...
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Chapter
Run-Time Exploitation of Application Dynamism for Energy-Efficient Exascale Computing
As in the embedded systems domain, energy efficiency has recently become one of the main design criteria in high performance computing. The European Union Horizon 2020 project READEX (Run-time Exploitation of ...
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Reference Work Entry In depth
Numerical Methods for the Fractional Differential Equations of Viscoelasticity
Mathematical models based on differential operators of fractional order have proven to be very useful for describing the properties of viscoelastic materials. However, the associated differential equations can...
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Living Reference Work Entry In depth
Numerical Methods for the Fractional Differential Equations of Viscoelasticity
Mathematical models based on differential operators of fractional order have proven to be very useful for describing the properties of viscoelastic materials. However, the associated differential equations can...
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Article
Erratum: The mean value theorems and a Nagumo-type uniqueness theorem for Caputo’s fractional calculus
In some of the statements of the author’s paper “The mean value theorems and a Nagumo-type uniqueness theorem for Caputo’s fractional calculus” (Fract. Calc. Appl. Anal. 15, No 2 (2012), pp. 304–313), a factor α ...
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Article
Asymptotic behavior of solutions of linear multi-order fractional differential systems
In this paper, we investigate some aspects of the qualitative theory for multi-order fractional differential equation systems. First, we obtain a fundamental result on the existence and uniqueness for multi-or...
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Article
Open AccessThe READEX formalism for automatic tuning for energy efficiency
Energy efficiency is an important aspect of future exascale systems, mainly due to rising energy cost. Although High performance computing (HPC) applications are compute centric, they still exhibit varying com...
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Article
Monotonicity of Functions and Sign Changes of Their Caputo Derivatives
It is well known that a continuously differentiable function is monotone in an interval [a, b] if and only if its first derivative does not change its sign there. We prove that this is equivalent to requiring tha...
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Article
A fractional calculus based model for the simulation of an outbreak of dengue fever
We propose a new mathematical model for the simulation of the dynamics of a dengue fever outbreak. Our model differs from the classical model in that it involves nonlinear differential equations of fractional,...
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Article
The mean value theorems and a Nagumo-type uniqueness theorem for Caputo’s fractional calculus
We generalize the classical mean value theorem of differential calculus by allowing the use of a Caputo-type fractional derivative instead of the commonly used first-order derivative. Similarly, we generalize ...
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Chapter and Conference Paper
Score-P: A Unified Performance Measurement System for Petascale Applications
The rapidly growing number of cores on modern supercomputers imposes scalability demands not only on applications but also on the software tools needed for their development. At the same time, increasing appli...
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Chapter and Conference Paper
Score-P: A Joint Performance Measurement Run-Time Infrastructure for Periscope, Scalasca, TAU, and Vampir
This paper gives an overview about the Score-P performance measurement infrastructure which is being jointly developed by leading HPC performance tools groups. It motivates the advantages of the joint undertak...
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Article
An efficient parallel algorithm for the numerical solution of fractional differential equations
The numerical solution of differential equations of fractional order is known to be a computationally very expensive problem due to the nonlocal nature of the fractional differential operators. We demonstrate ...
