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math.CA2020★ 155 cited
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-…
math.CA2017★ 1 cited
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…