• Corpus ID: 219559146

The fractional derivative of the Dirac delta function and new results on the inverse Laplace transform of irrational functions

  title={The fractional derivative of the Dirac delta function and new results on the inverse Laplace transform of irrational functions},
  author={Nicos Makris},
  journal={arXiv: Mathematical Physics},
  • Nicos Makris
  • Published 8 June 2020
  • Mathematics
  • arXiv: Mathematical Physics
Motivated from studies on anomalous diffusion, we show that the memory function $M(t)$ of complex materials, that their creep compliance follows a power law, $J(t)\sim t^q$ with $q\in \mathbb{R}^+$, is the fractional derivative of the Dirac delta function, $\frac{\mathrm{d}^q\delta(t-0)}{\mathrm{d}t^q}$ with $q\in \mathbb{R}^+$. This leads to the finding that the inverse Laplace transform of $s^q$ for any $q\in \mathbb{R}^+$ is the fractional derivative of the Dirac delta function, $\frac… 
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