155 citations · 487 across the 17 of their papers we have counts for
9 papers · 1 filter
Asymptotic behaviour of solutions to non-commensurate fractional-order planar systems
Kai Diethelm, Ha Duc Thai, Hoang The Tuan
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…
Upper and lower estimates for the separation of solutions to fractional differential equations
Kai Diethelm, Hoang The Tuan
Given a fractional differential equation of order with Caputo derivatives, we investigate in a quantitative sense how the associated solutions depend on their respecti…
Trends, Directions for Further Research, and Some Open Problems of Fractional Calculus
Kai Diethelm, Virginia Kiryakova, Yuri Luchko +2
The area of fractional calculus (FC) has been fast developing and is presently being applied in all scientific fields. Therefore, it is of key relevance to assess the present state…
Why fractional derivatives with nonsingular kernels should not be used
Kai Diethelm, Roberto Garrappa, Andrea Giusti +1
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-…
An Analytic and Numerical Analysis of Weighted Singular Cauchy Integrals with Exponential Weights on
S. B. Damelin, K. Diethelm
This paper concerns an analytic and numerical analysis of a class of weighted singular Cauchy integrals with exponential weights with finite moments and with smooth e…
The mean value theorems and a Nagumo-type uniqueness theorem for Caputo's fractional calculus (Corrected Version)
Kai Diethelm
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 derivati…
Asymptotic behavior of solutions of linear multi-order fractional differential equation systems
Kai Diethelm, Stefan Siegmund, H. T. Tuan
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 existenc…
Monotonicity of functions and sign changes of their Caputo derivatives
Kai Diethelm
It is well known that a continuously differentiable function is monotone in an interval if and only if its first derivative does not change its sign there. We prove that th…
An Extension of the Well-Posedness Concept for Fractional Differential Equations of Caputo's Type
Kai Diethelm
It is well known that, under standard assumptions, initial value problems for fractional ordinary differential equations involving Caputo-type derivatives are well posed in the sen…