Cauchy fractional derivative

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In this paper, we introduce a new sort of fractional derivative. For this, we consider the Cauchy's integral formula for derivatives and modify it by using Laplace transform. So, we obtain the fractional derivative formula F(α)(s) = L{(-1)(α)L-1{F(s)}}. Also, we find a relation between Weyl's fractional derivative and the formula above. Finally, we give some examples for fractional derivative of some elementary functions.

Weyl's fractional derivative, fractional calculus, laplace transform, cauchy's integral formula for derivatives

Короткий адрес:

IDR: 147232853   |   DOI: 10.14529/mmph200403

Список литературы Cauchy fractional derivative

  • Raina, R.K. On Weyl Fractional Calculus / R.K. Raina, C.L. Koul // Proc. Amer. Math. Soc. - 1979. - Vol. 73, no. 2. - P. 188-192.
  • Debnath, L. Integral Transforms and Their Applications / L. Debnath, D. Bhatta. - CRC press, Boca Raton, 2014. - 818 p.
  • Ahlfors, V.L. Complex Analysis / V.L. Ahlfors. - McGraw-Hill Inc., New York, 1979. - 336 p.
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